Palindromic Numbers other than Base 10

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Introduction

Palindromic numbers are numbers which read the same from

left to right (forwards) as from the right to left (backwards)

Here are a few random examples : 7, 3113, 44611644

Go directly to the Base 2 to Base 60 - with gaps - Tables topic
Go directly to the Base 2 Messages topic

Palindromic in Base 10 and Bases 2 to 60 - with gaps

Tables

Index Nr	Also palindromic in base 2 (binary) A007632	L base 10	L base 2
	Next > [183]
183	9794258529088310956256765905095676526590138809258524979	55	183
182	7992515739300692681583388637368833851862960039375152997	55	183
181	5982107767230157388234011419141104328837510327677012895	55	182
180	5750352680855632597679040581850409767952365580862530575	55	182
179	5500130929952642025961499398939941695202462599290310055	55	182
178	5375810570128326670426378465648736240766238210750185735	55	182
177	1610250372237506394572456221226542754936057322730520161	55	181
176	141608322140499819558130089980031855918994041223806141	54	177
175	98269568061626490790443471917434409709462616086596289	53	177
174	96974333658798698186600459595400668189689785633347969	53	177
173	74107193679989476350632192529123605367498997639170147	53	176
172	38042682015138742476430662826603467424783151028624083	53	175
171	14290800261309297950160720602706105979290316200809241	53	174
170	11583408501354096073227429192472237069045310580438511	53	173
169	3329456979344803072321377337731232703084439796549233	52	172
168	1894500919149741184783894664983874811479419190054981	52	171
167	1671376559622765380050133113310500835672269556731761	52	171
166	546590550388169569066255343552660965961883055095645	51	169
165	544889901625422417825862090268528714224526109988445	51	169
164	349755095251390482672234414432276284093152590557943	51	168
163	308714513290492817327216515612723718294092315417803	51	168
162	128426799107797312365090999090563213797701997624821	51	167
161	9142687306518774468290258520928644778156037862419	49	163
160	7109242970502610649115178715119460162050792429017	49	163
159	1873893355166996611906735376091166996615533983781	49	161
158	597817365870480462496846648694264084078563718795	48	159
157	502186653128032879493361163394978230821356681205	48	159
156	102735644379963218861031130168812369973446537201	48	157
155	78737696079148631316169196161313684197069673787	47	156
154	74953152103456169263148284136296165430125135947	47	156
153	72830033748815722240681118604222751884733003827	47	156
152	72224512737657344148643434684144375673721542227	47	156
151	56243939994005432191600400619123450049993934265	47	156
150	36755925874534219715185758151791243547852955763	47	155
149	16422159001061376847917371974867316010095122461	47	154
148	12328899531897059171731113717195079813599882321	47	154
147	9335388324586156026843333486206516854238835339	46	153
146	5318935032766104711807997081174016672305398135	46	152
145	903240486809073407096959690704370908684042309	45	150
144	706400325289926993853434358399629982523004607	45	149
143	557019370941199612258585852216991149073910755	45	149
142	9101547767757547725021205277457577677451019	43	143
141	7342779513978827245484845427288793159772437	43	143
140	3381578420704603001613161003064070248751833	43	142
139	1816060344791285708869688075821974430606181	43	141
138	905357630732463833436634338364237036753509	42	140
137	595943598626320807905509708023626895349595	42	139
136	309612431907274418544445814472709134216903	42	138
135	170341815153453197154451791354351518143071	42	137
134	139035351443367699760067996763344153530931	42	137
133	128795669673344381770077183443376966597821	42	137
132	98801466348600079992129997000684366410889	41	137
131	56545858306667087923432978076660385854565	41	136
130	38090421176450233778487733205467112409083	41	135
129	31636759764024794204540249742046795763613	41	135
128	14327425216354951264146215945361252472341	41	134
127	7114907950920173924554293710290597094117	40	133
126	1634587141488515712882175158841417854361	40	131
125	1017421766189445102992015449816671247101	40	130
124	773609618198307097595790703891816906377	39	130
123	551700061998405245575542504899160007155	39	129
122	131674457014330218696812033410754476131	39	127
121	124192421350471300727003174053124291421	39	127
120	122240824002234545959545432200428042221	39	127
119	32190158233101105022050110133285109123	38	125
118	9970387454991896491946981994547830799	37	123
117	9707999142717984907094897172419997079	37	123
116	5893890080115984244424895110800983985	37	123
115	1681824725831390428240931385274281861	37	121
114	1323475457008895965695988007545743231	37	120
113	998021119318189842248981813911120899	36	120
112	794397832642722540045227246238793497	36	120
111	710084230446469950059964644032480017	36	120
110	139124355701640720027046107553421931	36	117
109	96754720977532710701723577902745769	36	117
108	94285848717805140304150871784858249	36	117
107	76759778311938325452383911387795767	36	116
106	54074940541725088788052714504947045	36	116
105	10827628430039640604693003482672801	36	114
104	10652099006552766666725560099025601	36	114
103	9932525402284695775964822045252399	35	113
102	1480869563960100770010693659680841	35	111
101	1409460884147943003497414880649041	35	111
100	579782100975917393719579001287975	34	109
99	332997156422555464555224651799233	33	109
98	188726493036450333054630394627881	33	108
97	7155681676104835384016761865517	31	103
96	3390741646331381831336461470933	31	102
95	1115792035060833380605302975111	31	100
94	378059787464677776464787950873	30	99
93	56532345659072227095654323565	29	96
92	30658464822225352222846485603	29	95
91	30000258151173237115185200003	29	95
90	19756291244127372144219265791	29	94
89	17869806142184248124160896871	29	94
88	1609061098335005338901609061	28	91
87	795280629691202196926082597	27	90
86	552963956270141072659369255	27	89
85	532079161251434152161970235	27	89
84	Prime Curios! 390714505091666190505417093	27	89
83	351095331428353824133590153	27	89
82	138758321383797383123857831	27	87
81	50824513851188115831542805	26	86
80	7475703079870789703075747	25	83
79	7260988688520258868890627	25	83
78	5812988563013103658892185	25	83
77	1219228158701078518229121	25	81
76	1194313761393931673134911	25	80
75	1130486074817184706840311	25	80
74	94261805583838550816249	23	77
73	92913401775957710431929	23	77
72	72928088195859188082927	23	76
71	17461998948684989916471	23	74
70	539475328171823574935	21	69
69	114354126121621453411	21	67
68	94778157422475187749	20	67
67	32889941788714998823	20	65
66	10879740244204797801	20	64
65	9674868723278684769	19	64
64	7036267126217626307	19	63
63	313558153351855313	18	59
62	161206152251602161	18	58
61	55952637073625955	17	56
60	37629927072992673	17	56
59	37078796869787073	17	56
58	34104482028440143	17	55
57	18279440804497281	17	55
56	10819671917691801	17	54
55	10457587478575401	17	54
54	3148955775598413	16	52
53	1793770770773971	16	51
52	933138363831339	15	50
51	552212535212255	15	49
50	34141388314143	14	45
49	9484874784849	13	44
48	Prime Curios! 7284717174827	13	43
47	7227526257227	13	43
46	5652622262565	13	43
45	1999925299991	13	41
44	1794096904971	13	41
43	1792704072971	13	41
42	1474922294741	13	41
41	1413899983141	13	41
40	1234104014321	13	41
39	136525525631	12	37
38	110948849011	12	37
37	75015151057	11	37
36	32479297423	11	35
35	18462126481	11	35
34	10050905001	11	34
33	7451111547	10	33
32	1290880921	10	31
31	939474939	9	30
30	910373019	9	30
29	719848917	9	30
28	13500531	8	24
27	5841485	7	23
26	5259525	7	23
25	5071705	7	23
24	3129213	7	22
23	1979791	7	21
22	1934391	7	21
21	1758571	7	21
20	585585	6	20
19	73737	5	17
18	53835	5	16
17	53235	5	16
16	39993	5	16
15	32223	5	15
14	15351	5	14
13	9009	4	14
12	7447	4	13
11	717	3	10
10	585	3	10
9	Prime Curios! 313	3	9
8	99	2	7
7	33	2	6
6	9	1	4
5	Prime! 7	1	3
4	Prime! 5	1	3
3	Prime! 3	1	2
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 3 (ternary) A007633	L base 10	L base 3
	Next > 10^23
74	29397375542624557379392	23	48
73	26365450743834705456362	23	47
72	12241986986968968914221	23	47
71	2874264042112404624782	22	45
70	821697400030004796128	21	44
69	671028608646806820176	21	44
68	277444488080884444772	21	43
67	134137835777538731431	21	43
66	125556514464415655521	21	43
65	65691169644696119656	20	42
64	17706590033009560771	20	41
63	6942498569658942496	19	40
62	4054962560652694504	19	40
61	Prime! 3195269530359625913	19	39
60	2746827231327286472	19	39
59	2283864176714683822	19	39
58	659295875578592956	18	38
57	424676146641676424	18	37
56	354164182281461453	18	37
55	248480984489084842	18	37
54	65192854245829156	17	36
53	21669625852696612	17	35
52	21075228182257012	17	35
51	1984267447624891	16	33
50	534174353471435	15	31
49	438222212222834	15	31
48	69490044009496	14	30
47	6852190912586	13	27
46	5972209022795	13	27
45	4978471748794	13	27
44	4657098907564	13	27
43	4320048400234	13	27
42	2121010101212	13	26
41	81234543218	11	23
40	58049094085	11	23
39	2518338152	10	20
38	885626588	9	19
37	520080025	9	19
36	387505783	9	19
35	239060932	9	18
34	211131112	9	18
33	123464321	9	17
32	Prime! 112969211	9	17
31	83155138	8	17
30	27711772	8	16
29	Prime! 7949497	7	15
28	7875787	7	15
27	5737375	7	15
26	4287824	7	14
25	4251524	7	14
24	4219124	7	14
23	4022204	7	14
22	2985892	7	14
21	1521251	7	13
20	848848	6	13
19	Prime! 93739	5	11
18	92929	5	11
17	76267	5	11
16	75457	5	11
15	74647	5	11
14	48884	5	10
13	29092	5	10
12	Prime! 757	3	7
11	656	3	6
10	484	3	6
9	242	3	5
8	212	3	5
7	Prime! 151	3	5
6	121	3	5
5	8	1	2
4	4	1	2
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 4 A029961	L base 10	L base 4
	Next > 10^34
99	7179388640860660330660680468839717	34	57
98	5108871198905577557755098911788015	34	56
97	994887846928401212104829648788499	33	55
96	831689027065710434017560720986138	33	55
95	681970163682115333511286361079186	33	55
94	582281078505704363407505870182285	33	55
93	562496915896771070177698519694265	33	55
92	372432716388987767789883617234273	33	55
91	60036324544335099053344542363006	32	53
90	31197674993704500540739947679113	32	53
89	5435741640249592959420461475345	31	52
88	1875014103448187818443014105781	31	51
87	1871235782426682866242875321781	31	51
86	1816218002915034305192008126181	31	51
85	545349408734694496437804943545	30	50
84	92792216149502820594161229729	29	49
83	15821048498880208889484012851	29	47
82	7778107491576446751947018777	28	47
81	666101379010252010973101666	27	45
80	541144382839404938283441145	27	45
79	353061698367474763896160353	27	45
78	336725943608707806349527633	27	45
77	35852144650688605644125853	26	43
76	5667740260737370620477665	25	42
75	5644977785034305877794465	25	42
74	5205366624977794266635025	25	42
73	5072939121521251219392705	25	42
72	1622633305817185033362261	25	41
71	224769553250052355967422	24	39
70	149265574723327475562941	24	39
69	109895081241142180598901	24	39
68	98996197452425479169989	23	39
67	59923211850205811232995	23	38
66	59737594200100249573795	23	38
65	57410264882528846201475	23	38
64	874218768525867812478	21	35
63	830935451626154539038	21	35
62	819177862404268771918	21	35
61	542737478606874737245	21	35
60	371765223161322567173	21	35
59	317920613282316029713	21	35
58	43982928355382928934	20	33
57	41378114300341187314	20	33
56	5808197420247918085	19	32
55	5452702834382072545	19	32
54	3896203035303026983	19	31
53	3614621407041264163	19	31
52	3610232617162320163	19	31
51	Prime! 1270237235327320721	19	31
50	101882796697288101	18	29
49	96062045454026069	17	29
48	57264776467746275	17	28
47	55934950005943955	17	28
46	13585963536958531	17	27
45	7145572222755417	16	27
44	912702454207219	15	25
43	815969141969518	15	25
42	646219242912646	15	25
41	41830077003814	14	23
40	5690277720965	13	22
39	3445416145443	13	21
38	1649061609461	13	21
37	1491278721941	13	21
36	508152251805	12	20
35	506802208605	12	20
34	Prime! 73979697937	11	19
33	59201610295	11	18
32	53406060435	11	18
31	51717171715	11	18
30	954656459	9	15
29	623010326	9	15
28	53822835	8	13
27	5679765	7	12
26	5614165	7	12
25	5297925	7	12
24	5259525	7	12
23	5226225	7	12
22	5051505	7	12
21	3866683	7	11
20	Prime! 3826283	7	11
19	2215122	7	11
18	1801081	7	11
17	506605	6	10
16	57675	5	8
15	55655	5	8
14	55255	5	8
13	53235	5	8
12	7997	4	7
11	939	3	5
10	Prime! 787	3	5
9	666	3	5
8	393	3	5
7	Prime! 373	3	5
6	55	2	3
5	Prime! 5	1	2
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 5 A029962	L base 10	L base 5
	Next > 10^65
235	99543624930708890704741862774786868747726814740709880703942634599	65	93
234	99147784312541604654976982616872327861628967945640614521348774199	65	93
233	6328602704926148022920974990772442770994790292208416294072068236	64	92
232	3214064425866839870550144501476006741054410550789386685244604123	64	91
231	1194298706261022647836038501203773021058306387462201626078924911	64	91
230	64246994130107791610563653101711710135636501619770103149964246	62	89
229	64246947151782073152069988044044044088996025137028715174964246	62	89
228	6726055113244810012075917310121210137195702100184423115506276	61	88
227	1537290958777611519852104788359538874012589151167778590927351	61	87
226	1532805993046939711317225597922297955227131179396403995082351	61	87
225	883356191198880777154229788401104887922451777088891191653388	60	86
224	855387148635738589348806089598895980608843985837536841783558	60	86
223	65611982177205547205464612752725721646450274550277128911656	59	85
222	49066470901871197820861535773837753516802879117810907466094	59	84
221	46564717781637429651286018560906581068215692473618771746564	59	84
220	46193204666936421034725056580608565052743012463966640239164	59	84
219	26819889378948503897349399266566299394379830584987398891862	59	84
218	26819327009787305648386096848684869068384650378790072391862	59	84
217	26429470394241104810070078034443087007001840114249307492462	59	84
216	23505993486869791222414191577177519141422219796868439950532	59	84
215	23505101759336115455443641282328214634455451163395710150532	59	84
214	23110716142491983043006607134643170660034038919424161701132	59	84
213	9939319018903649287536637142992417366357829463098109139399	58	83
212	9663532981431429183577455753113575547753819241341892353669	58	83
211	323992966009823764929890740888047098929467328900669299323	57	81
210	147607387738648286008522726555627225800682846837783706741	57	81
209	147479499604608433501150032393230051105334806406994974741	57	81
208	143388662988323740825383628646826383528047323889266883341	57	81
207	143321023950291019441762870959078267144910192059320123341	57	81
206	119863297658330074654226108000801622456470033856792368911	57	81
205	119628570830560390462705268656862507264093065038075826911	57	81
204	Prime! 7278175677249196711781595411145951871176919427765718727	55	79
203	7273374492984432327579333256523339757232344892944733727	55	79
202	7222664231853227887310973231323790137887223581324662227	55	79
201	6432766862954931730863303210123033680371394592686672346	55	79
200	85716526225965980181166063136066118108956952262561758	53	76
199	85716017941173123289734017871043798232137114971061758	53	76
198	85716017477430276081758313031385718067203477471061758	53	76
197	82804167487745127987827179797172878972154778476140828	53	76
196	4677402018132779160228780990878220619772318102047764	52	74
195	842273089643651424746389343983647424156346980372248	51	73
194	842273084433104837434610484016434738401334480372248	51	73
193	842226914944632453620370868073026354236449419622248	51	73
192	14866415178804123258016455461085232140887151466841	50	71
191	14453303304094582613377100177331628549040330335441	50	71
190	649936241751591323106805508601323195157142639946	48	69
189	644863400626259088360013310063880952626004368446	48	69
188	18946467978107252552707370725525270187976464981	47	67
187	18443384607066153566982628966535166070648334481	47	67
186	15431793058951766720187878102766715985039713451	47	67
185	15088344815041421175663836657112414051844388051	47	67
184	15083888608839064281812521818246093880688838051	47	67
183	628697035925578552616888616255875529530796826	45	65
182	623253838747288310488898884013882747838352326	45	65
181	623206113631461755935454539557164136311602326	45	65
180	453749841231167144063656360441761132148947354	45	64
179	453511538505603587495626594785306505835115354	45	64
178	299610806696519408825434528804915696608016992	45	64
177	299610383727266016934646439610662727383016992	45	64
176	295964701807089636010787010636980708107469592	45	64
175	295282435673135443681676186344531376534282592	45	64
174	266201850128363317817101718713363821058102662	45	64
173	98966828061040971279788797217904016082866989	44	63
172	98912606618485761310633601316758481660621989	44	63
171	84086672007102503839977993830520170027668048	44	63
170	81240685713569129553899835592196531758604218	44	63
169	6011032286710901481210121841090176822301106	43	62
168	4277593255207257584473744857527025523957724	43	61
167	4270026508536613602272722063166358056200724	43	61
166	4236754831325615292754572925165231384576324	43	61
165	4236708500824894032575752304984280058076324	43	61
164	2426494758641569264741474629651468574946242	43	61
163	2426494706658461989505059891648566074946242	43	61
162	2181439476143709144546454419073416749341812	43	61
161	2147108966833950371150511730593386698017412	43	61
160	2106935294299775474599954745779924925396012	43	61
159	2106902281191302045590955402031911822096012	43	61
158	1416696065500088921662661298800055606966141	43	61
157	1414883972971911767319137671191792793884141	43	61
156	1010331096582278428458548248722856901330101	43	61
155	64515508991444322135253122344419980551546	41	59
154	61153138639139701434943410793193683135116	41	59
153	879878999661878204161402878166999878978	39	56
152	879348262202819129818921918202262843978	39	56
151	45958282654026060755706062045628285954	38	54
150	9835554837464633869683364647384555389	37	53
149	9596045768849458689868549488675406959	37	53
148	9505227132110846796976480112317225059	37	53
147	8467638770573174655564713750778367648	37	53
146	8183225575843802043402083485755223818	37	53
145	8145978316763435541455343676138795418	37	53
144	8140197799388539232329358839977910418	37	53
143	685120603841801367763108148306021586	36	52
142	602117076566221263362122665670711206	36	52
141	215355547165064584485460561745553512	36	51
140	106007162214551780087155412261700601	36	51
139	7748092041062101661012601402908477	34	49
138	6950267776950891441980596777620596	34	49
137	186838521546391111193645125838681	33	47
136	186162880909630434036909088261681	33	47
135	186162396111968171869111693261681	33	47
134	159171014284036444630482410171951	33	47
133	151998543003841676148300345899151	33	47
132	151998059721974171479127950899151	33	47
131	87653343665645377354656634335678	32	46
130	6297024459737003007379544207926	31	45
129	6292788805324353534235088872926	31	45
128	4572400421665334335661240042754	31	44
127	920049038842450054248830940029	30	43
126	863908970332451154233079809368	30	43
125	68123866829364346392866832186	29	42
124	60795457035659595653075459706	29	42
123	41618751128915351982115781614	29	41
122	31891884714945654941748819813	29	41
121	31417977787079697078777971413	29	41
120	31417972547345054374527971413	29	41
119	31416063242381218324236061413	29	41
118	31098164866494349466846189013	29	41
117	31029154725081318052745192013	29	41
116	24055999711386268311799955042	29	41
115	14626535770963836907753562641	29	41
114	10644461464435453446416444601	29	41
113	10233317539812221893571333201	29	41
112	775981910664202466019189577	27	39
111	775939410541000145014939577	27	39
110	775934282861868168282439577	27	39
109	691774458431323134854477196	27	39
108	618762750915151519057267816	27	39
107	613119004633151336400911316	27	39
106	18652160016866861006125681	26	37
105	15636166151988915166163651	26	37
104	15631144307799770344113651	26	37
103	8785720289021209820275878	25	36
102	679116049774477940611976	24	35
101	89750520757375702505798	23	33
100	89750054183338145005798	23	33
99	89707442492029424470798	23	33
98	89378795951815959787398	23	33
97	89373703300800330737398	23	33
96	89373235305150353237398	23	33
95	86985339391719393358968	23	33
94	86980677074747077608968	23	33
93	86502759048484095720568	23	33
92	86502714378987341720568	23	33
91	83732343311311334323738	23	33
90	83208975695159657980238	23	33
89	83208405647274650480238	23	33
88	4185459800880089545814	22	31
87	3441731791881971371443	22	31
86	2015496835005386945102	22	31
85	1073077634334367703701	22	31
84	1071727595775957271701	22	31
83	69258642177124685296	20	29
82	66819814955941891866	20	29
81	61034375000057343016	20	29
80	22192753388335729122	20	28
79	1877026246426207781	19	27
78	1872666725276662781	19	27
77	1872168528258612781	19	27
76	1560890621260980651	19	27
75	1560393839383930651	19	27
74	1527447408047447251	19	27
73	67546323432364576	17	25
72	62596751915769526	17	25
71	28453146364135482	17	24
70	28012639493621082	17	24
69	25856101110165852	17	24
68	25851377577315852	17	24
67	8671162112611768	16	23
66	8066449229446608	16	23
65	8061113993111608	16	23
64	658768979867856	15	22
63	653311040113356	15	22
62	473696969696374	15	21
61	473643646346374	15	21
60	449933929339944	15	21
59	449488282884944	15	21
58	445389595983544	15	21
57	445384969483544	15	21
56	445336272633544	15	21
55	378573424375873	15	21
54	374476969674473	15	21
53	301537434735103	15	21
52	279119383911972	15	21
51	206903565309602	15	21
50	206725444527602	15	21
49	202304515403202	15	21
48	176265757562671	15	21
47	176071838170671	15	21
46	172849181948271	15	21
45	172102080201271	15	21
44	132412434214231	15	21
43	107793080397701	15	21
42	107745787547701	15	21
41	103824717428301	15	21
40	103191131191301	15	21
39	7730173710377	13	19
38	6989062609896	13	19
37	6982578752896	13	19
36	6694978794966	13	19
35	6648130318466	13	19
34	6643369633466	13	19
33	6105769675016	13	19
32	2228261628222	13	18
31	12185058121	11	15
30	12114741121	11	15
29	6761551676	10	15
28	2893553982	10	14
27	2596886952	10	14
26	2512882152	10	14
25	836181638	9	13
24	836131638	9	13
23	831868138	9	13
22	831333138	9	13
21	808656808	9	13
20	65977956	8	12
19	47633674	8	11
18	30322303	8	11
17	27711772	8	11
16	10400401	8	11
15	10088001	8	11
14	18881	5	7
13	15751	5	7
12	1221	4	5
11	676	3	5
10	626	3	5
9	282	3	4
8	252	3	4
7	88	2	3
6	6	1	2
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 6 A029963	L base 10	L base 6
	Next > 10^23
118	Prime! 36599233807670833299563	23	29
117	33461025859695852016433	23	29
116	32046696937973969664023	23	29
115	31442983675957638924413	23	29
114	27596928275057282969572	23	29
113	26387697060106079678362	23	29
112	4800062971441792600084	22	28
111	3951300420330240031593	22	28
110	3228607293993927068223	22	28
109	954705277777772507459	21	27
108	698624223676322426896	21	27
107	515942802363208249515	21	27
106	413110328121823011314	21	27
105	184042927656729240481	21	27
104	101486113646311684101	21	26
103	80695452588525459608	20	26
102	5761547475747451675	19	25
101	5283511046401153825	19	25
100	617599427724995716	18	23
99	76123829292832167	17	22
98	65332462626423356	17	22
97	63799978687999736	17	22
96	34283490709438243	17	22
95	14459868686895441	17	21
94	14441050405014441	17	21
93	12907568886570921	17	21
92	8020863443680208	16	21
91	5796663883666975	16	21
90	2806592662956082	16	20
89	900893585398009	15	20
88	596437282734695	15	19
87	585789323987585	15	19
86	521151929151125	15	19
85	480680444086084	15	19
84	422383797383224	15	19
83	395921848129593	15	19
82	389019363910983	15	19
81	359630212036953	15	19
80	309491626194903	15	19
79	285666464666582	15	19
78	Prime! 155259838952551	15	19
77	80839044093808	14	18
76	51910622601915	14	18
75	41443999934414	14	18
74	10268799786201	14	17
73	9766560656679	13	17
72	8288882888828	13	17
71	6873812183786	13	17
70	3695202025963	13	17
69	3693222223963	13	17
68	3691422241963	13	17
67	3666926296663	13	17
66	1808482848081	13	16
65	75535653557	11	14
64	71771717717	11	14
63	61662426616	11	14
62	18013531081	11	14
61	12482428421	11	13
60	Prime! 11271517211	11	13
59	8801331088	10	13
58	7786556877	10	13
57	7111881117	10	13
56	4368778634	10	13
55	3733113373	10	13
54	342050243	9	11
53	310393013	9	11
52	290222092	9	11
51	Prime! 108151801	9	11
50	104888401	9	11
49	103656301	9	11
48	24466442	8	10
47	15266251	8	10
46	9081809	7	9
45	8164618	7	9
44	6983896	7	9
43	6934396	7	9
42	6901096	7	9
41	5799975	7	9
40	5766675	7	9
39	5733375	7	9
38	5482845	7	9
37	5433345	7	9
36	5400045	7	9
35	5182815	7	9
34	5100015	7	9
33	4849484	7	9
32	4598954	7	9
31	4565654	7	9
30	4516154	7	9
29	4298924	7	9
28	4265624	7	9
27	4232324	7	9
26	3097903	7	9
25	1867681	7	9
24	909909	6	8
23	808808	6	8
22	168861	6	7
21	74647	5	7
20	39893	5	6
19	22022	5	6
18	7777	4	6
17	7667	4	5
16	1441	4	5
15	868	3	4
14	777	3	4
13	434	3	4
12	343	3	4
11	Prime! 191	3	3
10	141	3	3
9	111	3	3
8	55	2	3
7	Prime! 7	1	2
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 7 A029964	L base 10	L base 7
	Next > 10^23
81	67949117406960471194976	23	28
80	65437371449594417373456	23	27
79	47019576850605867591074	23	27
78	29627836901610963872692	23	27
77	24392712895759821729342	23	27
76	20722521562726512522702	23	27
75	Prime! 17797767519791576779771	23	27
74	8421198978888798911248	22	26
73	942538532686235835249	21	25
72	755667017939710766557	21	25
71	617161162878261161716	21	25
70	507598924909429895705	21	25
69	400003717000717300004	21	25
68	397793140060041397793	21	25
67	240176399252993671042	21	25
66	22244818422481844222	20	23
65	9100681853581860019	19	23
64	7869047624267409687	19	23
63	99739047074093799	17	21
62	98709855955890789	17	21
61	67122911011922176	17	20
60	65045053335054056	17	20
59	42074205350247024	17	20
58	7584718778174857	16	19
57	3179862222689713	16	19
56	229716363617922	15	17
55	215821424128512	15	17
54	208063959360802	15	17
53	201946010649102	15	17
52	85161755716158	14	17
51	74194966949147	14	17
50	49929477492994	14	17
49	23419766791432	14	16
48	8868067608688	13	16
47	6750989890576	13	16
46	4158563658514	13	15
45	2928299928292	13	15
44	2745382835472	13	15
43	2680120210862	13	154
42	2451956591542	13	15
41	2264092904622	13	15
40	1269880889621	13	15
39	775350053577	12	15
38	426970079624	12	14
37	95365056359	11	13
36	91023932019	11	13
35	Prime! 90750705709	11	13
34	75431213457	11	13
33	75016161057	11	13
32	65796069756	11	13
31	64454545446	11	13
30	61454945416	11	13
29	45862226854	11	13
28	40130703104	11	13
27	25699499652	11	13
26	858474858	9	11
25	657494756	9	11
24	638828836	9	11
23	485494584	9	11
22	466828664	9	11
21	230474032	9	10
20	61255216	8	10
19	Prime! 9470749	7	9
18	6958596	7	9
17	6597956	7	9
16	4602064	7	8
15	2137312	7	8
14	65656	5	6
13	Prime! 16561	5	5
12	292	3	3
11	242	3	3
10	171	3	3
9	121	3	3
8	8	1	2
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 8 (octal) A029804	L base 10	L base 8
	Next > 10^34
131	6091280052696093663906962500821906	34	38
130	1141897415190856226580915147981411	34	37
129	994090604572440313044275406090499	33	37
128	858037680965763515367569086730858	33	37
127	835523283332531656135233382325538	33	37
126	587617843046963898369640348716785	33	37
125	564341093237119818911732390143465	33	37
124	355309407484416525614484704903553	33	37
123	89879768957194388349175986797898	32	36
122	38525491344366033066344319452583	32	35
121	17181377425940999904952477318171	32	35
120	3792033197162477742617913302973	31	34
119	3377242440477033307740442427733	31	34
118	2903795477478606068747745973092	31	34
117	1949700108422995992248010079491	31	34
116	98444861536975557963516844489	29	33
115	79443858725719191752785834497	29	33
114	68607705200272427200250770686	29	32
113	62119978192296969229187991126	29	32
112	36386515691205650219651568363	29	32
111	20466353976385158367935366402	29	32
110	2674972302079669702032794762	28	31
109	619057787673525376787750916	27	30
108	138668092301868103290866831	27	29
107	107184009820444028900481701	27	29
106	82268662917644671926686228	26	29
105	41155431112055021113455114	26	29
104	9504411213036303121144059	25	28
103	9502917646378736467192059	25	28
102	9500465760922290675640059	25	28
101	6857776528536358256777586	25	28
100	3760849013081803109480673	25	28
99	2091103570615160753011902	25	27
98	1646819988303038899186461	25	27
97	890170268088880862071098	24	27
96	315610027864468720016513	24	27
95	39752656623032665625793	23	26
94	36258340143534104385263	23	25
93	Prime! 34125703495359430752143	23	25
92	17395259698289695259371	23	25
91	15863125024242052136851	23	25
90	7393237064774607323937	22	25
89	2503498805115088943052	22	24
88	579927810111018729975	21	23
87	556362998454899263655	21	23
86	552868393727393868255	21	23
85	494635531909135536494	21	23
84	473317002010200713374	21	23
83	379080765242567080973	21	23
82	375586160515061685573	21	23
81	375183597404795381573	21	23
80	371911868919868119173	21	23
79	202693712161217396202	21	23
78	77580854944945808577	20	23
77	44643103022030134644	20	22
76	32300361188116300323	20	22
75	9843207767677023489	19	22
74	3800003150513000083	19	21
73	3676077166617706763	19	21
72	2650626939396260562	19	21
71	2445420079700245442	19	21
70	1219071169611709121	19	21
69	136053358853350631	18	19
68	105080469964080501	18	19
67	96876827472867869	17	19
66	84199148484199148	17	19
65	84172361516327148	17	19
64	70333341514333307	17	19
63	57234017271043275	17	19
62	45576210301267554	17	19
61	45534430503443554	17	19
60	33239024742093233	17	19
59	685854414458586	15	17
58	683113474311386	15	17
57	666551535155666	15	17
56	393073414370393	15	17
55	359934111439953	15	17
54	224785646587422	15	16
53	185850999058581	15	16
52	112745383547211	15	16
51	34926999962943	14	15
50	28719555591782	14	15
49	13994688649931	14	15
48	7712150512177	13	15
47	5853143413585	13	15
46	5227529257225	13	15
45	390894498093	12	13
44	294378873492	12	13
43	94466666449	11	13
42	94029892049	11	13
41	20855555802	11	12
40	4637337364	10	11
39	4480880844	10	11
38	4424994244	10	11
37	2464554642	10	11
36	1820330281	10	11
35	799535997	9	10
34	719848917	9	10
33	532898235	9	10
32	130535031	9	9
31	55366355	8	9
30	4198914	7	8
29	Prime! 1970791	7	7
28	1935391	7	7
27	Prime! 1496941	7	7
26	660066	6	7
25	628826	6	7
24	207702	6	6
23	30303	5	5
22	Prime! 30103	5	5
21	26662	5	5
20	26462	5	5
19	Prime! 13331	5	5
18	13131	5	5
17	8778	4	5
16	3663	4	4
15	585	3	4
14	414	3	3
13	Prime! 373	3	3
12	333	3	3
11	292	3	3
10	121	3	3
9	9	1	2
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 9 A029965	L base 10	L base 9
	Next > 10^23
75	7623722153663512273267	22	23
74	4997878480660848787994	22	23
73	3014849211991129484103	22	23
72	1895043293663923405981	22	23
71	1685380415005140835861	22	23
70	104618510424015816401	21	21
69	89349349588594394398	20	21
68	82148829699692884128	20	21
67	53293648433484639235	20	21
66	547906983389609745	18	19
65	194216405504612491	18	19
64	190076027720670091	18	19
63	14802554345520841	17	17
62	13577478487477531	17	17
61	11199701210799111	17	17
60	11111059395011111	17	17
59	5987078778707895	16	17
58	4782537117352874	16	17
57	149819212918941	15	15
56	149285434582941	15	15
55	101904010409101	15	15
54	42143900934124	14	15
53	41275222257214	14	15
52	2081985891802	13	13
51	2024099904202	13	13
50	2005542455002	13	13
49	Prime! 1400232320041	13	13
48	827362263728	12	13
47	9565335659	10	11
46	8901111098	10	11
45	5435665345	10	11
44	382000283	9	9
43	232000232	9	9
42	181434181	9	9
41	167191761	9	9
40	65666656	8	9
39	3360633	7	7
38	3303033	7	7
37	3171713	7	7
36	3163613	7	7
35	3122213	7	7
34	3114113	7	7
33	Prime! 3106013	7	7
32	2450542	7	7
31	2442442	7	7
30	2434342	7	7
29	2401042	7	7
28	1885881	7	7
27	1877781	7	7
26	1828281	7	7
25	1721271	7	7
24	1713171	7	7
23	1540451	7	7
22	626626	6	7
21	50605	5	5
20	42324	5	5
19	27472	5	5
18	25752	5	5
17	6886	4	5
16	656	3	3
15	646	3	3
14	555	3	3
13	464	3	3
12	Prime! 373	3	3
11	282	3	3
10	Prime! 191	3	3
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 11 A029966	L base 10	L base 11
	Next > 10^21
83	903253059636950352309	21	21
82	771341832818238143177	21	21
81	686833076121670338686	21	21
80	671136738666837631176	21	20
79	7861736017106371687	19	19
78	6411682614162861146	19	19
77	4244691467641964424	19	18
76	64224652625642246	17	17
75	62712119691121726	17	17
74	56831729892713865	17	17
73	56681764446718665	17	17
72	54470642224607445	17	17
71	463906656609364	15	15
70	259799383997952	15	14
69	251569181965152	15	14
68	218254595452812	15	14
67	218210353012812	15	14
66	218053292350812	15	14
65	4798641468974	13	13
64	2926072706292	13	12
63	2909278729092	13	12
62	42521012524	11	11
61	39453235493	11	11
60	39276067293	11	11
59	Prime! 999454999	9	9
58	Prime! 998111899	9	9
57	537181735	9	9
56	492080294	9	9
55	489525984	9	9
54	362151263	9	9
53	356777653	9	9
52	8844488	7	7
51	8832388	7	7
50	8820288	7	7
49	8758578	7	7
48	8746478	7	7
47	8734378	7	7
46	8722278	7	7
45	8710178	7	7
44	7292927	7	7
43	7280827	7	7
42	5741475	7	7
41	5667665	7	7
40	5655565	7	7
39	5643465	7	7
38	4593954	7	7
37	4581854	7	7
36	4422244	7	7
35	4410144	7	7
34	4348434	7	7
33	3372733	7	7
32	3360633	7	7
31	3298923	7	7
30	Prime! 3286823	7	7
29	3274723	7	7
28	3262623	7	7
27	2968692	7	7
26	2956592	7	7
25	75157	5	5
24	63936	5	5
23	52825	5	5
22	49294	5	5
21	40504	5	5
20	Prime! 38183	5	5
19	26962	5	5
18	909	3	3
17	898	3	3
16	Prime! 787	3	3
15	676	3	3
14	565	3	3
13	454	3	3
12	343	3	3
11	232	3	3
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 12 A029967	L base 10	L base 12
	Next > 10^21
61	302002264282462200203	21	19
60	283631008131800136382	21	19
59	216811149242941118612	21	19
58	52975769933996757925	20	19
57	3967113331333117693	19	18
56	3345454646464545433	19	18
55	1834592905092954381	19	17
54	1312161375731612131	19	17
53	1310127138317210131	19	17
52	926617966669716629	18	17
51	418955743347559814	18	17
50	411528847748825114	18	17
49	90145891619854109	17	16
48	16330182728103361	17	16
47	8330107227010338	16	15
46	5128288228828215	16	15
45	1643600330063461	16	15
44	62218411481226	14	13
43	10171466417101	14	13
42	4538684868354	13	12
41	357496694753	12	11
40	122507705221	12	11
39	73183838137	11	11
38	57644144675	11	10
37	50992729905	11	10
36	36265856263	11	10
35	25712321752	11	10
34	1393223931	10	9
33	796212697	9	9
32	Prime! 713171317	9	9
31	520020025	9	9
30	293373392	9	8
29	139979931	9	8
28	133373331	9	8
27	9963699	7	7
26	8364638	7	7
25	5641465	7	7
24	3192913	7	7
23	646646	6	6
22	88888	5	5
21	43934	5	5
20	35953	5	5
19	8008	4	4
18	1111	4	3
17	Prime! 797	3	3
16	737	3	3
15	676	3	3
14	616	3	3
13	555	3	3
12	Prime! 181	3	3
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 13 A029968	L base 10	L base 13
	Next > 10^21
86	995165177898771561599	21	19
85	Prime! 970015486464684510079	21	19
84	960085137626731580069	21	19
83	958539908323809935859	21	19
82	931953637343736359139	21	19
81	832587648262846785238	21	19
80	364370458757854073463	21	19
79	292503721141127305292	21	19
78	277258880242088852772	21	19
77	162238140040041832261	21	19
76	Prime! 7520859392939580257	19	17
75	5544882623262884455	19	17
74	4002414299924142004	19	17
73	3976149369639416793	19	17
72	3898701537351078983	19	17
71	2832604939394062382	19	17
70	1836905795975096381	19	17
69	49164413731446194	17	15
68	45850453835405854	17	15
67	37079407070497073	17	15
66	7273324774233727	16	15
65	672804838408276	15	14
64	637013161310736	15	14
63	237923878329732	15	13
62	235604838406532	15	13
61	60808311380806	14	13
60	54324199142345	14	13
59	1624981894261	13	11
58	1199309039911	13	11
57	789679976987	12	11
56	22087878022	11	10
55	8390660938	10	9
54	8381551838	10	9
53	7497557947	10	9
52	7488448847	10	9
51	6933223396	10	9
50	6924114296	10	9
49	4378778734	10	9
48	4369669634	10	9
47	3814444183	10	9
46	3805335083	10	9
45	3071001703	10	9
44	952404259	9	9
43	668666866	9	8
42	656353656	9	8
41	62611626	8	7
40	47099074	8	7
39	44166144	8	7
38	33299233	8	7
37	23877832	8	7
36	23177132	8	7
35	20944902	8	7
34	20244202	8	7
33	13055031	8	7
32	10122101	8	7
31	8864688	7	7
30	2906092	7	6
29	2832382	7	6
28	2713172	7	6
27	2377732	7	6
26	311113	6	5
25	56265	5	5
24	26362	5	4
23	25452	5	4
22	24542	5	4
21	8778	4	4
20	6776	4	4
19	1111	4	3
18	Prime! 797	3	3
17	666	3	3
16	575	3	3
15	444	3	3
14	Prime! 353	3	3
13	Prime! 313	3	3
12	222	3	3
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 14 A029969	L base 10	L base 14
	Next >10^21
78	756517966373669715657	21	19
77	535729030313030927535	21	19
76	531011782080287110135	21	19
75	59380193522539108395	20	18
74	59236342599524363295	20	18
73	26916102000020161962	20	17
72	15595183733738159551	20	17
71	15319521066012591351	20	17
70	7327284858584827237	19	17
69	7209611033301169027	19	17
68	6158981849481898516	19	17
67	6114506601066054116	19	17
66	6005359623269535006	19	17
65	3737334250524337373	19	17
64	3545494238324945453	19	17
63	546546033330645645	18	16
62	78325277777252387	17	15
61	69580792329708596	17	15
60	68300282528200386	17	15
59	57047363236374075	17	15
58	26072218381227062	17	15
57	24514444744441542	17	15
56	13955648684655931	17	15
55	5902037117302095	16	14
54	765611080116567	15	13
53	756559989955657	15	13
52	692021131120296	15	13
51	611552272255116	15	13
50	475794747497574	15	13
49	306149949941603	15	13
48	253675545576352	15	13
47	236070676070632	15	13
46	5813343433185	13	12
45	5542179712455	13	12
44	5530138310355	13	12
43	5507474747055	13	12
42	5105070705015	13	12
41	3984321234893	13	11
40	2428022208242	13	11
39	1098445448901	13	11
38	1031186811301	13	11
37	695256652596	12	11
36	549905509945	12	11
35	518032230815	12	11
34	508628826805	12	11
33	17085058071	11	9
32	Prime! 14203330241	11	9
31	11652825611	11	9
30	10476867401	11	9
29	6758008576	10	9
28	5736116375	10	9
27	595121595	9	8
26	564303465	9	8
25	535505535	9	8
24	9813189	7	7
23	9578759	7	7
22	Prime! 9046409	7	7
21	546645	6	6
20	420024	6	5
19	59095	5	5
18	39593	5	5
17	1111	4	3
16	999	3	3
15	858	3	3
14	717	3	3
13	464	3	3
12	323	3	3
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 15 A029970	L base 10	L base 15
	Next > 10^20
73	89551457844875415598	20	17
72	6747920044400297476	19	17
71	6736942564652496376	19	17
70	4038582985892858304	19	16
69	427791895598197724	18	15
68	194176722227671491	18	15
67	74940172027104947	17	15
66	Prime! 74713184748131747	17	15
65	74712906560921747	17	15
64	74712663536621747	17	15
63	284111151111482	15	13
62	283652313256382	15	13
61	141527282725141	15	13
60	42629999992624	14	12
59	40700399300704	14	12
58	8004830384008	13	11
57	7485535355847	13	11
56	7305480845037	13	11
55	7073218123707	13	11
54	7073152513707	13	11
53	6908732378096	13	11
52	6907268627096	13	11
51	6799415149976	13	11
50	6637917197366	13	11
49	6624883884266	13	11
48	6624024204266	13	11
47	6498409048946	13	11
46	6498343438946	13	11
45	5938567658395	13	11
44	1131877781311	13	11
43	1131018101311	13	11
42	692465564296	12	11
41	615221122516	12	11
40	20281518202	11	9
39	17406960471	11	9
38	8083223808	10	9
37	8052662508	10	9
36	8050880508	10	9
35	2118008112	10	8
34	69455496	8	7
33	47999974	8	7
32	39399393	8	7
31	28300382	8	7
30	26144162	8	7
29	17577571	8	7
28	527725	6	5
27	515515	6	5
26	489984	6	5
25	477774	6	5
24	465564	6	5
23	67576	5	5
22	60106	5	5
21	25552	5	4
20	23632	5	4
19	2772	4	3
18	1551	4	3
17	979	3	3
16	949	3	3
15	Prime! 919	3	3
14	888	3	3
13	858	3	3
12	828	3	3
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 16 A029731	L base 10	L base 16
	Next > 10^35
143	78894191945563376367336554919149887	35	29
142	67080932508181062626018180523908076	35	29
141	63835882500017943434971000528853836	35	29
140	63494339670590336663309507693349436	35	29
139	57486792197841346664314879129768475	35	29
138	46494289039985405650458993098249464	35	29
137	36453210513649714141794631501235463	35	29
136	25295130572966082928066927503159252	35	29
135	17193090890651737173715609809039171	35	29
134	589179652669993373399966256971985	33	28
133	324193060418058060850814060391423	33	27
132	322434305921054020450129503434223	33	27
131	188980399889523060325988993089881	33	27
130	157124568577706949607775865421751	33	27
129	153570961886167878761688169075351	33	27
128	74310782571520833802517528701347	32	27
127	47204048169521688612596184040274	32	27
126	9578569814271350531724189658759	31	26
125	7308855736123322233216375588037	31	26
124	1097029772441563651442779207901	31	25
123	494506253843744447348352605494	30	25
122	94694284038931313983048249649	29	25
121	94635334973676267637943353649	29	25
120	92167013075480608457031076129	29	25
119	17173681623264946232618637171	29	24
118	4526239847945445497489326254	28	23
117	4374175479923993299745714734	28	23
116	2092577007449999447007752902	28	23
115	875288502888989888205882578	27	23
114	374178087384212483780871473	27	23
113	319895202367858763202598913	27	23
112	107761099424686424990167701	27	22
111	107527175676494676571725701	27	22
110	43231887066299266078813234	26	22
109	37264989541299214598946273	26	22
108	9133129628211128269213319	25	21
107	1846781136065606311876481	25	21
106	Prime! 1844238058789878508324481	25	21
105	1829860070497940700689281	25	21
104	1013945256196916525493101	25	20
103	66346948489298484964366	23	19
102	55582430128882103428555	23	19
101	51959301115851110395915	23	19
100	47844728597079582744874	23	19
99	47272007451015470027274	23	19
98	42001490723332709410024	23	19
97	36039109398989390193063	23	19
96	34570154169596145107543	23	19
95	34175825152525152857143	23	19
94	28527697711011779672582	23	19
93	21471020918081902017412	23	19
92	17322666253735266622371	23	19
91	15673605260306250637651	23	19
90	873954892151298459378	21	18
89	264605616858616506462	21	17
88	180766294494492667081	21	17
87	136228674727476822631	21	17
86	134132582494285231431	21	17
85	109640971252179046901	21	17
84	105086879868978680501	21	17
83	70701884511548810707	20	17
82	41317967000076971314	20	17
81	4616159308039516164	19	16
80	3884425716175244883	19	16
79	1137081002001807311	19	15
78	1118494603064948111	19	15
77	887358331133853788	18	15
76	535873916619378535	18	15
75	373019805508910373	18	15
74	70667820502876607	17	14
73	64634327472343646	17	14
72	32633196169133623	17	14
71	32000428082400023	17	14
70	5099347667439905	16	14
69	1668739779378661	16	13
68	816346555643618	15	13
67	522013020310225	15	13
66	509538666835905	15	13
65	Prime! 397922151229793	15	13
64	45113388331154	14	12
63	17262755726271	14	11
62	14315822851341	14	11
61	7888195918887	13	11
60	6694367634966	13	11
59	Prime! 3405684865043	13	11
58	2692667662962	13	11
57	2424058504242	13	11
56	1806872786081	13	11
55	1631645461361	13	11
54	1278169618721	13	11
53	390189981093	12	10
52	56702120765	11	9
51	51113531115	11	9
50	45961216954	11	9
49	43836363834	11	9
48	39762526793	11	9
47	32442924423	11	9
46	30144644103	11	9
45	28779897782	11	9
44	28586268582	11	9
43	26896769862	11	9
42	247969742	9	7
41	241090142	9	7
40	Prime! 190080091	9	7
39	161131161	9	7
38	119919911	9	7
37	94544549	8	7
36	94355349	8	7
35	90999909	8	7
34	67433476	8	7
33	9616169	7	6
32	6487846	7	6
31	5614165	7	6
30	2485842	7	6
29	1612161	7	6
28	845548	6	5
27	749947	6	5
26	666666	6	5
25	512215	6	5
24	333333	6	5
23	Prime! 98689	5	5
22	96369	5	5
21	Prime! 94049	5	5
20	90209	5	5
19	41514	5	4
18	39593	5	4
17	3003	4	3
16	1991	4	3
15	979	3	3
14	Prime! 787	3	3
13	626	3	3
12	Prime! 353	3	3
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 17 A097855	L base 10	L base 17
	Next > 10^20
70	4552204672764022554	19	16
69	2552577177717752552	19	15
68	1561203188813021651	19	15
67	763504480084405367	18	15
66	395414871178414593	18	15
65	327224207702422723	18	15
64	174670389983076471	18	15
63	85437364146373458	17	14
62	47548262526284574	17	14
61	41285701710758214	17	14
60	40101963636910104	17	14
59	29287621712678292	17	14
58	20378349094387302	17	14
57	7351755005571537	16	13
56	6905270220725096	16	13
55	965201404102569	15	13
54	406631878136604	15	12
53	19038433483091	14	11
52	14705022050741	14	11
51	4244405044424	13	11
50	650880088056	12	10
49	494280082494	12	10
48	493533335394	12	10
47	98794149789	11	9
46	91792829719	11	9
45	77991919977	11	9
44	72603630627	11	9
43	68921312986	11	9
42	58802720885	11	9
41	57431913475	11	9
40	30873037803	11	9
39	2038558302	10	8
38	335929533	9	7
37	280535082	9	7
36	229232922	9	7
35	212313212	9	7
34	208373802	9	7
33	207535702	9	7
32	124454421	9	7
31	123616321	9	7
30	103595301	9	7
29	102757201	9	7
28	31744713	8	7
27	8837388	7	6
26	4165614	7	6
25	1388831	7	5
24	335533	6	5
23	256652	6	5
22	177771	6	5
21	94249	5	5
20	61416	5	4
19	4554	4	3
18	2882	4	3
17	989	3	3
16	818	3	3
15	767	3	3
14	545	3	3
13	494	3	3
12	252	3	2
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 18 A248889	L base 10	L base 18
	Next > 10^20
83	41470196888869107414	20	16
82	5827580384830857285	19	15
81	5812958640468592185	19	15
80	5725600893980065275	19	15
79	5052817248427182505	19	15
78	4804809688869084084	19	15
77	3497509383839057943	19	15
76	3489855513155589843	19	15
75	3377352952592537733	19	15
74	2528468040408648252	19	15
73	2525541666661455252	19	15
72	2432426921296242342	19	15
71	2324074260624704232	19	15
70	1884584402044854881	19	15
69	1129798206028979211	19	15
68	104737165561737401	18	14
67	18245601610654281	17	13
66	11247779597774211	17	13
65	4725393553935274	16	13
64	4671431331341764	16	13
63	3496774224776943	16	13
62	1511668448661151	16	13
61	427740777047724	15	12
60	385281878182583	15	12
59	56203688630265	14	11
58	35334455443353	14	11
57	5764436344675	13	11
56	3968412148693	13	11
55	3376963696733	13	10
54	2557615167552	13	10
53	188833338881	12	9
52	Prime! 79288288297	11	9
51	69675357696	11	9
50	59388288395	11	9
49	58813031885	11	9
48	26965056962	11	9
47	14969696941	11	9
46	387191783	9	7
45	Prime! 386454683	9	7
44	385717583	9	7
43	376222673	9	7
42	327696723	9	7
41	326959623	9	7
40	221050122	9	7
39	220313022	9	7
38	191010191	9	7
37	118919811	9	7
36	88844888	8	7
35	55499455	8	7
34	54411445	8	7
33	39388393	8	7
32	Prime! 1832381	7	5
31	1403041	7	5
30	1254521	7	5
29	981189	6	5
28	859958	6	5
27	782287	6	5
26	583385	6	5
25	262262	6	5
24	69996	5	4
23	46664	5	4
22	23332	5	4
21	3773	4	3
20	2112	4	3
19	1661	4	3
18	848	3	3
17	686	3	3
16	595	3	3
15	505	3	3
14	343	3	3
13	323	3	2
12	171	3	2
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 19 A248899	L base 10	L base 19
	Next > 10^20
60	11330422577522403311	20	15
59	9611176039306711169	19	15
58	9333120815180213339	19	15
57	8705115152515115078	19	15
56	8507775490945777058	19	15
55	7401130704070311047	19	15
54	7382719398939172837	19	15
53	6510099759579900156	19	15
52	5846194156514916485	19	15
51	4502146351536412054	19	15
50	4306351929291536034	19	15
49	3695653224223565963	19	15
48	41530875757803514	17	13
47	33670675157607633	17	13
46	30676982028967603	17	13
45	21858850305885812	17	13
44	18057661216675081	17	13
43	10365316861356301	17	13
42	8328654774568238	16	13
41	2794478998744972	16	13
40	2696617447166962	16	13
39	6976862686796	13	11
38	6959926299596	13	11
37	246025520642	12	9
36	234595595432	12	9
35	139103301931	12	9
34	127673376721	12	9
33	121791197121	12	9
32	96060106069	11	9
31	87161116178	11	9
30	67269596276	11	9
29	62558085526	11	9
28	47069796074	11	9
27	863828368	9	7
26	857383758	9	7
25	666909666	9	7
24	650767056	9	7
23	467535764	9	7
22	453848354	9	7
21	Prime! 330050033	9	7
20	Prime! 155292551	9	7
19	2211122	7	5
18	1897981	7	5
17	Prime! 1551551	7	5
16	864468	6	5
15	432234	6	5
14	1771	4	3
13	838	3	3
12	666	3	3
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 20 A250408	L base 10	L base 20
	Next > 10^20
85	105878013310878501	18	14
84	71874813431847817	17	13
83	71831895259813817	17	13
82	69517556065571596	17	13
81	69515054645051596	17	13
80	69515035653051596	17	13
79	67316423732461376	17	13
78	67316404740461376	17	13
77	67314157075141376	17	13
76	67182731613728176	17	13
75	67180087178008176	17	13
74	2533637117363352	16	12
73	2533401331043352	16	12
72	115629444926511	15	11
71	115488939884511	15	11
70	115482777284511	15	11
69	115482161284511	15	11
68	115238181832511	15	11
67	112989686989211	15	11
66	112983848389211	15	11
65	112739252937211	15	11
64	112733414337211	15	11
63	112733090337211	15	11
62	96757333375769	14	11
61	96544000044569	14	11
60	92862200226829	14	11
59	86356300365368	14	11
58	82885700758828	14	11
57	82868066086828	14	11
56	76185311358167	14	11
55	76160000006167	14	11
54	72697077079627	14	11
53	72691155119627	14	11
52	72678611687627	14	11
51	72279011097227	14	11
50	68857077075886	14	11
49	68851155115886	14	11
48	68838611683886	14	11
47	62296044069226	14	11
46	62089899898026	14	11
45	58667622676685	14	11
44	58661700716685	14	11
43	58456044065485	14	11
42	54985444458945	14	11
41	48479922997484	14	11
40	48473077037484	14	11
39	44778355387744	14	11
38	44584411448544	14	11
37	38283622638283	14	11
36	38072044027083	14	11
35	28095922959082	14	11
34	14102600620141	14	11
33	10614366341601	14	11
32	355746647553	12	9
31	355110011553	12	9
30	334843348433	12	9
29	334495594433	12	9
28	1444884441	10	8
27	1919191	7	5
26	Prime! 1917191	7	5
25	1915191	7	5
24	1913191	7	5
23	1788871	7	5
22	1786871	7	5
21	1784871	7	5
20	30303	5	4
19	22722	5	4
18	20202	5	4
17	12621	5	4
16	10101	5	4
15	7117	4	3
14	6776	4	3
13	6556	4	3
12	252	3	2
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 21	L base 10	L base 21
	Next > 10^20
105	54022659711795622045	20	15
104	53479116322361197435	20	15
103	52695119366391159625	20	15
102	32056623722732665023	20	15
101	28130792022029703182	20	15
100	4889312521252139884	19	15
99	2969386212126839692	19	14
98	2745161405041615472	19	14
97	2407431827281347042	19	14
96	2242598563658952422	19	14
95	881866612216668188	18	14
94	478303605506303874	18	14
93	99703025352030799	17	13
92	92613604440631629	17	13
91	82993441914439928	17	13
90	Prime! 78357734643775387	17	13
89	49126258185262194	17	13
88	44506740304760544	17	13
87	39823252625232893	17	13
86	38275424142457283	17	13
85	37022794049722073	17	13
84	32924868186842923	17	13
83	28590052425009582	17	13
82	23530366466303532	17	13
81	13894950405949831	17	13
80	10091495959419001	17	13
79	8628788338878268	16	13
78	6388598118958836	16	12
77	6116292442926116	16	12
76	4690638558360964	16	12
75	2369324774239632	16	12
74	2277486006847722	16	12
73	881910212019188	15	12
72	338734909437833	15	11
71	289911959119982	15	11
70	235023626320532	15	11
69	217306686603712	15	11
68	207449545944702	15	11
67	128197515791821	15	11
66	90660677606609	14	11
65	59139544593195	14	11
64	27210988901272	14	11
63	8816817186188	13	10
62	2596329236952	13	10
61	440827728044	12	9
60	303880088303	12	9
59	98157575189	11	9
58	79375957397	11	9
57	66969496966	11	9
56	54482928445	11	9
55	8087337808	10	8
54	6801661086	10	8
53	4672002764	10	8
52	4475555744	10	8
51	2130880312	10	8
50	1696776961	10	7
49	1418668141	10	7
48	1378448731	10	7
47	900535009	9	7
46	620282026	9	7
45	490222094	9	7
44	427020724	9	7
43	423484324	9	7
42	409161904	9	7
41	340373043	9	7
40	293080392	9	7
39	68933986	8	6
38	67222276	8	6
37	66988966	8	6
36	46422464	8	6
35	28355382	8	6
34	25622652	8	6
33	6612166	7	6
32	6563656	7	6
31	6233326	7	6
30	3979793	7	5
29	3735373	7	5
28	3710173	7	5
27	2379732	7	5
26	1844481	7	5
25	845548	6	5
24	672276	6	5
23	203302	6	5
22	87978	5	4
21	61116	5	4
20	989	3	3
19	Prime! 757	3	3
18	505	3	3
17	484	3	3
16	242	3	2
15	88	2	2
14	66	2	2
13	44	2	2
12	22	2	2
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 22	L base 10	L base 22
	Next > 10^20
72	74312996511569921347	20	15
71	72673811666611837627	20	15
70	72413971722717931427	20	15
69	72099151411415199027	20	15
68	71670186944968107617	20	15
67	7260302291922030627	19	15
66	150917442244719051	18	13
65	142054031130450241	18	13
64	95881569296518859	17	13
63	93895494749459839	17	13
62	90814147874141809	17	13
61	89233276667233298	17	13
60	89079044444097098	17	13
59	83218001210081238	17	13
58	75144757675744157	17	13
57	71360959395906317	17	13
56	19291952825919291	17	13
55	17467113931176471	17	13
54	574128141821475	15	11
53	573859747958375	15	11
52	567425595524765	15	11
51	495172868271594	15	11
50	276695727596672	15	11
49	232474888474232	15	11
48	145410535014541	15	11
47	100357979753001	15	11
46	1963232323691	13	10
45	1389924299831	13	10
44	1162319132611	13	9
43	93648984639	11	9
42	77263836277	11	9
41	77185658177	11	9
40	Prime! 75293639257	11	9
39	18486568481	11	8
38	1297007921	10	7
37	1285665821	10	7
36	575595575	9	7
35	575232575	9	7
34	472181274	9	7
33	399080993	9	7
32	133727331	9	7
31	59155195	8	6
30	5109015	7	5
29	5048405	7	5
28	2968692	7	5
27	2846482	7	5
26	2408042	7	5
25	2359532	7	5
24	79097	5	4
23	76567	5	4
22	28382	5	4
21	25852	5	4
20	5775	4	3
19	5665	4	3
18	5555	4	3
17	5445	4	3
16	5335	4	3
15	Prime! 727	3	3
14	595	3	3
13	414	3	2
12	161	3	2
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 23	L base 10	L base 23
	Next > 10^20
75	8210665697965660128	19	14
74	4816500789870056184	19	14
73	4283464631364643824	19	14
72	487917888888719784	18	13
71	306274366663472603	18	13
70	87947524442574978	17	13
69	81157437573475118	17	13
68	75427181318172457	17	13
67	30110838583801103	17	13
66	870451686154078	15	11
65	854161737161458	15	11
64	771958868859177	15	11
63	743564333465347	15	11
62	743067525760347	15	11
61	595175959571595	15	11
60	583400171004385	15	11
59	567110222011765	15	11
58	439321919123934	15	11
57	274078272870472	15	11
56	156776767677651	15	11
55	144645535546441	15	11
54	144148727841441	15	11
53	59568111186595	14	11
52	8463508053648	13	10
51	1759179719571	13	9
50	1724384834271	13	9
49	1372149412731	13	9
48	881274472188	12	9
47	830493394038	12	9
46	676421124676	12	9
45	638980089836	12	9
44	625640046526	12	9
43	317227722713	12	9
42	63522022536	11	8
41	61029992016	11	8
40	46405150464	11	8
39	3181771813	10	7
38	2266116622	10	7
37	965585569	9	7
36	949969949	9	7
35	843636348	9	7
34	282565282	9	7
33	254040452	9	7
32	199757991	9	7
31	6307036	7	5
30	5836385	7	5
29	5116115	7	5
28	4645464	7	5
27	4151514	7	5
26	3454543	7	5
25	1911191	7	5
24	1049401	7	5
23	88488	5	4
22	84048	5	4
21	65256	5	4
20	42024	5	4
19	6336	4	3
18	5115	4	3
17	3663	4	3
16	2442	4	3
15	1221	4	3
14	898	3	3
13	737	3	3
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 24 A250409	L base 10	L base 24
	Next > 10^20
103	86812504855840521868	20	15
102	47620992166129902674	20	15
101	39763873222237836793	20	15
100	33847674500547674833	20	15
99	5219957301037599125	19	14
98	834291782287192438	18	13
97	830868275572868038	18	13
96	705673961169376507	18	13
95	689870646646078986	18	13
94	500807240042708005	18	13
93	351531099990135153	18	13
92	334935786687539433	18	13
91	56257511911575265	17	13
90	Prime! 37872782328727873	17	13
89	1081605445061801	16	11
88	978898787898879	15	11
87	974909929909479	15	11
86	972363696363279	15	11
85	893872555278398	15	11
84	893859050958398	15	11
83	Prime! 726674454476627	15	11
82	720623343326027	15	11
81	709277808772907	15	11
80	668444222444866	15	11
79	649470979074946	15	11
78	649457474754946	15	11
77	379849999948973	15	11
76	352084363480253	15	11
75	296430484034692	15	11
74	294823767328492	15	11
73	279033838330972	15	11
72	273593222395372	15	11
71	108971474179801	15	11
70	106395121593601	15	11
69	100344010443001	15	11
68	5223359533225	13	10
67	2084684864802	13	9
66	2084226224802	13	9
65	2024272724202	13	9
64	1490461640941	13	9
63	1318742478131	13	9
62	1047699967401	13	9
61	1042342432401	13	9
60	780089980087	12	9
59	686286682686	12	9
58	240745547042	12	9
57	129797797921	12	9
56	125825528521	12	9
55	3032112303	10	7
54	2315115132	10	7
53	1516776151	10	7
52	1039669301	10	7
51	981050189	9	7
50	866333668	9	7
49	760313067	9	7
48	728434827	9	7
47	491979194	9	7
46	459020954	9	7
45	417767714	9	7
44	353000353	9	7
43	311747113	9	7
42	Prime! 7865687	7	5
41	7658567	7	5
40	7192917	7	5
39	7132317	7	5
38	6747476	7	5
37	6281826	7	5
36	6014106	7	5
35	5836385	7	5
34	5103015	7	5
33	4925294	7	5
32	4296924	7	5
31	4029204	7	5
30	Prime! 3673763	7	5
29	3118113	7	5
28	2762672	7	5
27	2267622	7	5
26	2207022	7	5
25	Prime! 1851581	7	5
24	374473	6	5
23	13631	5	3
22	12621	5	3
21	11011	5	3
20	10001	5	3
19	8558	4	3
18	6996	4	3
17	6226	4	3
16	4664	4	3
15	2332	4	3
14	575	3	2
13	525	3	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 25 A250410	L base 10	L base 25
	Next > 10^20
96	77606803722730860677	20	15
95	62581772266227718526	20	15
94	Prime! 1272787016107872721	19	13
93	Prime! 1272398751578932721	19	13
92	Prime! 1272394497944932721	19	13
91	1262866576756682621	19	13
90	1262694643464962621	19	13
89	1262690389830962621	19	13
88	Prime! 1262585225225852621	19	13
87	1262196960696912621	19	13
86	Prime! 1262196953596912621	19	13
85	1252998152518992521	19	13
84	1252990535350992521	19	13
83	1252881117111882521	19	13
82	689560096690065986	18	13
81	109981264462189901	18	13
80	62005276067250026	17	13
79	8251018778101528	16	12
78	1134114554114311	16	11
77	858118262811858	15	11
76	854207131702458	15	11
75	659953777359956	15	11
74	606970919079606	15	11
73	507756707657705	15	11
72	404662313266404	15	11
71	404615656516404	15	11
70	400704525407004	15	11
69	309318434813903	15	11
68	259756919657952	15	11
67	255881999188552	15	11
66	255839929938552	15	11
65	251970868079152	15	11
64	206784282487602	15	11
63	206224040422602	15	11
62	202867292768202	15	11
61	202307050703202	15	11
60	156662525266651	15	11
59	89954955945998	14	10
58	89331400413398	14	10
57	61986277268916	14	10
56	28023488432082	14	10
55	1678753578761	13	9
54	Prime! 1678699968761	13	9
53	1678690968761	13	9
52	83895259838	11	8
51	83849694838	11	8
50	874868478	9	7
49	874383478	9	7
48	827777728	9	7
47	223454322	9	6
46	85400458	8	6
45	9498949	7	5
44	Prime! 9493949	7	5
43	9467649	7	5
42	9462649	7	5
41	9436349	7	5
40	9431349	7	5
39	9405049	7	5
38	Prime! 9400049	7	5
37	8986898	7	5
36	6639366	7	5
35	6634366	7	5
34	6608066	7	5
33	6603066	7	5
32	3397933	7	5
31	Prime! 3392933	7	5
30	3366633	7	5
29	3361633	7	5
28	3335333	7	5
27	3330333	7	5
26	3309033	7	5
25	Prime! 3304033	7	5
24	2859582	7	5
23	2828282	7	5
22	626626	6	5
21	622226	6	5
20	9339	4	3
19	8338	4	3
18	7887	4	3
17	6886	4	3
16	1001	4	3
15	676	3	3
14	626	3	3
13	494	3	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 26	L base 10	L base 26
	Next > 10^20
90	93028124222242182039	20	15
89	9767283178713827679	19	14
88	6996005035305006996	19	14
87	2334617912197164332	19	13
86	2162340330330432612	19	13
85	1897787568657877981	19	13
84	1139080380830809311	19	13
83	1056500659560056501	19	13
82	739608723327806937	18	13
81	95118076767081159	17	12
80	89973287278237998	17	12
79	3603830770383063	16	11
78	3603500110053063	16	11
77	3555977887795553	16	11
76	3555647227465553	16	11
75	1364785115874631	16	11
74	1009338558339001	16	11
73	889700474007988	15	11
72	889266565662988	15	11
71	873216272612378	15	11
70	738793101397837	15	11
69	722274868472227	15	11
68	612500656005216	15	11
67	520743626347025	15	11
66	512326979623215	15	11
65	420569949965024	15	11
64	179877909778971	15	11
63	106018868810601	15	10
62	103472686274301	15	10
61	92424066042429	14	10
60	5404902094045	13	9
59	5223922293225	13	9
58	4726136316274	13	9
57	4190117110914	13	9
56	3693694963963	13	9
55	3662197912663	13	9
54	Prime! 3610437340163	13	9
53	3335051505333	13	9
52	3193401043913	13	9
51	3146469646413	13	9
50	2183758573812	13	9
49	2149753579412	13	9
48	1181201021811	13	9
47	1134269624311	13	9
46	185076670581	12	8
45	72728282727	11	8
44	30966666903	11	8
43	6825225286	10	7
42	4417777144	10	7
41	2069559602	10	7
40	933242339	9	7
39	643090346	9	7
38	626262626	9	7
37	321131123	9	7
36	Prime! 319282913	9	7
35	238010832	9	6
34	218050812	9	6
33	134515431	9	6
32	9823289	7	5
31	9679769	7	5
30	8285828	7	5
29	7924297	7	5
28	6530356	7	5
27	5048405	7	5
26	4631364	7	5
25	1387831	7	5
24	84348	5	4
23	49194	5	4
22	18981	5	4
21	Prime! 17471	5	3
20	14841	5	3
19	Prime! 13331	5	3
18	10701	5	3
17	9009	4	3
16	8228	4	3
15	7447	4	3
14	4114	4	3
13	989	3	3
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 27 A250411	L base 10	L base 27
	Next > 10^20
84	3386694465644966833	19	13
83	3032960836380692303	19	13
82	2988046368636408892	19	13
81	2973882904092883792	19	13
80	2885566902096655882	19	13
79	2800354468644530082	19	13
78	2019923988893299102	19	13
77	Prime! 1975783979793875791	19	13
76	1905991653561995091	19	13
75	1800943129213490081	19	13
74	1653624894984263561	19	13
73	957001143341100759	18	13
72	752009074470900257	18	13
71	475084743347480574	18	13
70	295871648846178592	18	13
69	63240319091304236	17	12
68	3774273333724773	16	11
67	2533880440883352	16	11
66	1276149009416721	16	11
65	987115383511789	15	11
64	963217686712369	15	11
63	872951606159278	15	11
62	824685424586428	15	11
61	570984989489075	15	11
60	6041548451406	13	9
59	6014294924106	13	9
58	5779540459775	13	9
57	5193025203915	13	9
56	5052248422505	13	9
55	4806859586084	13	9
54	4725972795274	13	9
53	4520609060254	13	9
52	4446399936444	13	9
51	4280234320824	13	9
50	3958336338593	13	9
49	3817559557183	13	9
48	2969036309692	13	9
47	2904768674092	13	9
46	2823881883282	13	9
45	9058338509	10	7
44	8417447148	10	7
43	5364224635	10	7
42	2487997842	10	7
41	2132882312	10	7
40	836040638	9	7
39	609808906	9	7
38	214171412	9	6
37	67166176	8	6
36	9827289	7	5
35	9466649	7	5
34	9392939	7	5
33	8737378	7	5
32	8663668	7	5
31	7573757	7	5
30	7368637	7	5
29	6639366	7	5
28	6278726	7	5
27	5549455	7	5
26	5475745	7	5
25	4385834	7	5
24	2287822	7	5
23	1197911	7	5
22	65856	5	4
21	17871	5	3
20	15951	5	3
19	13031	5	3
18	Prime! 10301	5	3
17	Prime! 919	3	3
16	838	3	3
15	Prime! 757	3	3
14	616	3	2
13	252	3	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 28	L base 10	L base 28
	Next > 10^20
80	29518742877824781592	20	14
79	19799649566594699791	20	14
78	6242866325236682426	19	13
77	6215457749477545126	19	13
76	4875696356536965784	19	13
75	4380016867686100834	19	13
74	3961949609069491693	19	13
73	3601086475746801063	19	13
72	2988309751579038892	19	13
71	2918489161619848192	19	13
70	1747045084805407471	19	13
69	314435021120534413	18	13
68	20210235053201202	17	12
67	5249970550799425	16	11
66	918395696593819	15	11
65	850128939821058	15	11
64	629596242695926	15	11
63	548785939587845	15	11
62	525408828804525	15	11
61	319102262201913	15	11
60	54173144137145	14	10
59	9693965693969	13	9
58	8338331338338	13	9
57	8332192912338	13	9
56	6385093905836	13	9
55	5788955598875	13	9
54	4699722279964	13	9
53	4120874780214	13	9
52	Prime! 3597871787953	13	9
51	2636029206362	13	9
50	731212212137	12	9
49	396183381693	12	9
48	276220022672	12	8
47	89279097298	11	8
46	79124342197	11	8
45	13363136331	11	7
44	13240004231	11	7
43	11242524211	11	7
42	10549494501	11	7
41	7298118927	10	7
40	6175005716	10	7
39	5760110675	10	7
38	1538668351	10	7
37	Prime! 947141749	9	7
36	904171409	9	7
35	Prime! 773939377	9	7
34	Prime! 751585157	9	7
33	711757117	9	7
32	500595005	9	7
31	427777724	9	6
30	161040161	9	6
29	10499401	8	5
28	Prime! 9324239	7	5
27	8788878	7	5
26	7003007	7	5
25	6601066	7	5
24	6231326	7	5
23	5695965	7	5
22	2972792	7	5
21	20802	5	3
20	16961	5	3
19	15251	5	3
18	10401	5	3
17	6336	4	3
16	5775	4	3
15	696	3	2
14	464	3	2
13	232	3	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 29	L base 10	L base 29
	Next > 10^20
74	9697997765677997969	19	13
73	8524686215126864258	19	13
72	8371624840484261738	19	13
71	8321104265624011238	19	13
70	6552920373730292556	19	13
69	6429956023206599246	19	13
68	4403998032308993044	19	13
67	3624609808089064263	19	13
66	3351297118117921533	19	13
65	1818308821288038181	19	13
64	760804929929408067	18	13
63	Prime! 11696809290869611	17	11
62	7423932992393247	16	11
61	5268469009648625	16	11
60	2658767997678562	16	11
59	12102077020121	14	9
58	9852537352589	13	9
57	8991895981998	13	9
56	8939482849398	13	9
55	8775005005778	13	9
54	8511759571158	13	9
53	8361888881638	13	9
52	7696190916967	13	9
51	Prime! 7066183816607	13	9
50	7040427240407	13	9
49	6975552555796	13	9
48	6127372737216	13	9
47	5634774774365	13	9
46	5060470740605	13	9
45	4870236320784	13	9
44	4240229220424	13	9
43	4022056502204	13	9
42	Prime! 3957181817593	13	9
41	3301418141033	13	9
40	Prime! 3000234320003	13	9
39	2440776770442	13	9
38	Prime! 1145071705411	13	9
37	15865056851	11	7
36	15700600751	11	7
35	14914241941	11	7
34	14698289641	11	7
33	14533833541	11	7
32	5983223895	10	7
31	5255225525	10	7
30	4771771774	10	7
29	4043773404	10	7
28	693252396	9	7
27	9911199	7	5
26	9537359	7	5
25	8525258	7	5
24	Prime! 7958597	7	5
23	7139317	7	5
22	7078707	7	5
21	6233326	7	5
20	6172716	7	5
19	5160615	7	5
18	4654564	7	5
17	4593954	7	5
16	3581853	7	5
15	19191	5	3
14	1771	4	3
13	Prime! 929	3	3
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 30	L base 10	L base 30
	Next > 10^20
72	213121689986121312	18	12
71	212937009900739212	18	12
70	12602195859120621	17	11
69	509566626665905	15	10
68	487035171530784	15	10
67	239318080813932	15	10
66	238892545298832	15	10
65	14313300331341	14	9
64	Prime! 1201117111021	13	9
63	1201109011021	13	9
62	16004240061	11	7
61	15826462851	11	7
60	15599599551	11	7
59	15583138551	11	7
58	15347274351	11	7
57	2134994312	10	7
56	2127777212	10	7
55	1142992411	10	7
54	637888736	9	6
53	296878692	9	6
52	17433471	8	5
51	3178713	7	5
50	3161613	7	5
49	2402042	7	5
48	2293922	7	5
47	2285822	7	5
46	2277722	7	5
45	2269622	7	5
44	2102012	7	5
43	1501051	7	5
42	1392931	7	5
41	1384831	7	5
40	Prime! 1201021	7	5
39	Prime! 1092901	7	5
38	1084801	7	5
37	735537	6	4
36	20602	5	3
35	20302	5	3
34	20002	5	3
33	19791	5	3
32	19491	5	3
31	19191	5	3
30	18981	5	3
29	Prime! 10601	5	3
28	Prime! 10301	5	3
27	10001	5	3
26	7117	4	3
25	6006	4	3
24	5225	4	3
23	4444	4	3
22	4114	4	3
21	3333	4	3
20	3003	4	3
19	2552	4	3
18	2222	4	3
17	1771	4	3
16	1441	4	3
15	1111	4	3
14	868	3	2
13	434	3	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 31	L base 10	L base 31
	Next > 10^20
86	20360129533592106302	20	13
85	11450847544574805411	20	13
84	9517904104014097159	19	13
83	9459484661664849549	19	13
82	9270992260622990729	19	13
81	8432814151514182348	19	13
80	8092734322234372908	19	13
79	8017702574752077108	19	13
78	7879371694961739787	19	13
77	6852701184811072586	19	13
76	5597872726272787955	19	13
75	4077487289827847704	19	13
74	3467500900090057643	19	13
73	2747530935390357472	19	13
72	1828521298921258281	19	13
71	1227145498945417221	19	13
70	42269242224296224	17	12
69	24191783438719142	17	11
68	23762558085526732	17	11
67	15294534043549251	17	11
66	9917528008257199	16	11
65	8744740440474478	16	11
64	Prime! 961030858030169	15	11
63	831208202802138	15	11
62	673317949713376	15	10
61	635180616081536	15	10
60	616197474791616	15	10
59	19350999905391	14	9
58	18508300380581	14	9
57	Prime! 9115199915119	13	9
56	9028337338209	13	9
55	8760465640678	13	9
54	8605751575068	13	9
53	7707170717077	13	9
52	7511392931157	13	9
51	7225198915227	13	9
50	7138336338317	13	9
49	3406192916043	13	9
48	17039593071	11	7
47	Prime! 11819991811	11	7
46	1551551551	10	7
45	961909169	9	7
44	844252448	9	6
43	65200256	8	6
42	63999936	8	6
41	23900932	8	5
40	13333331	8	5
39	9151519	7	5
38	9030309	7	5
37	Prime! 7696967	7	5
36	7575757	7	5
35	7454547	7	5
34	6383836	7	5
33	6262626	7	5
32	6141416	7	5
31	6020206	7	5
30	4686864	7	5
29	3494943	7	5
28	3373733	7	5
27	Prime! 3252523	7	5
26	3131313	7	5
25	3010103	7	5
24	86368	5	4
23	40704	5	4
22	29792	5	4
21	23832	5	3
20	22622	5	3
19	21412	5	3
18	20202	5	3
17	Prime! 19891	5	3
16	18681	5	3
15	Prime! 17471	5	3
14	7447	4	3
13	1551	4	3
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 32 A099165	L base 10	L base 32
	Next > 10^20
120	81298451466415489218	20	14
119	52413912066021931425	20	14
118	50385737133173758305	20	14
117	50193942722724939105	20	14
116	23398054977945089332	20	13
115	5888361733371638885	19	13
114	4650111258521110564	19	13
113	2808927324237298082	19	13
112	2449080129210809442	19	13
111	776016912219610677	18	12
110	571259217712952175	18	12
109	465707571175707564	18	12
108	330774945549477033	18	12
107	112474443344474211	18	12
106	85491930303919458	17	12
105	33303935753930333	17	11
104	27630511811503672	17	11
103	27429643234692472	17	11
102	27402111411120472	17	11
101	Prime! 17624701910742671	17	11
100	17096171817169071	17	11
99	14777935853977741	17	11
98	13177885058877131	17	11
97	Prime! 13150353235305131	17	11
96	Prime! 10894711311749801	17	11
95	10603962026930601	17	11
94	10478015751087401	17	11
93	10263806360836201	17	11
92	3422669229662243	16	11
91	2869960660699682	16	11
90	2297158228517922	16	11
89	1278746666478721	16	11
88	1032078008702301	16	10
87	24916011061942	14	9
86	17438700783471	14	9
85	10641522514601	14	9
84	8867028207688	13	9
83	8842552552488	13	9
82	8825076705288	13	9
81	6886033306886	13	9
80	5842794972485	13	9
79	5806855586085	13	9
78	4462757572644	13	9
77	1462999992641	13	9
76	1232143412321	13	9
75	935448844539	12	8
74	846261162648	12	8
73	691647746196	12	8
72	494889988494	12	8
71	444036630444	12	8
70	421833338124	12	8
69	34318181343	11	7
68	18884748881	11	7
67	14311211341	11	7
66	10269296201	11	7
65	10261916201	11	7
64	8804774088	10	7
63	6806006086	10	7
62	3403003043	10	7
61	2880990882	10	7
60	1219669121	10	7
59	983767389	9	6
58	933909339	9	6
57	388919883	9	6
56	37477473	8	6
55	29800892	8	5
54	25777752	8	5
53	21499412	8	5
52	21033012	8	5
51	18255281	8	5
50	9867689	7	5
49	9802089	7	5
48	9658569	7	5
47	8407048	7	5
46	6882886	7	5
45	6673766	7	5
44	5487845	7	5
43	5422245	7	5
42	4236324	7	5
41	3825283	7	5
40	2639362	7	5
39	1251521	7	5
38	912219	6	4
37	804408	6	4
36	780087	6	4
35	717717	6	4
34	672276	6	4
33	609906	6	4
32	585585	6	4
31	564465	6	4
30	477774	6	4
29	369963	6	4
28	54945	5	4
27	32223	5	3
26	29692	5	3
25	21012	5	3
24	Prime! 19891	5	3
23	15951	5	3
22	9449	4	3
21	6886	4	3
20	5445	4	3
19	2882	4	3
18	1441	4	3
17	858	3	2
16	363	3	2
15	99	2	2
14	66	2	2
13	33	2	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 33	L base 10	L base 33
	Next > 10^20
67	38230911200211903283	20	13
66	37538898355389883573	20	13
65	19409402444420490491	20	13
64	18783954433445938781	20	13
63	9458721256521278549	19	13
62	6602041596951402066	19	13
61	4792519341439152974	19	13
60	3767693732373967673	19	13
59	3419314993994139143	19	13
58	3072610981890162703	19	13
57	49824185758142894	17	11
56	49398817071889394	17	11
55	43902061516020934	17	11
54	39190925052909193	17	11
53	26293112421139262	17	11
52	24361112521116342	17	11
51	22435712721753422	17	11
50	19255758085755291	17	11
49	681321878123186	15	10
48	7087281827807	13	9
47	5239168619325	13	9
46	3298767678923	13	9
45	3125102015213	13	9
44	2957779777592	13	9
43	2908060608092	13	9
42	2736923296372	13	9
41	40909290904	11	7
40	30817071803	11	7
39	28681818682	11	7
38	12483938421	11	7
37	610787016	9	6
36	26811862	8	5
35	26211262	8	5
34	14111141	8	5
33	9012109	7	5
32	7192917	7	5
31	6545456	7	5
30	5153515	7	5
29	4506054	7	5
28	3114113	7	5
27	2369632	7	5
26	Prime! 1820281	7	5
25	1294921	7	5
24	421124	6	4
23	415514	6	4
22	409904	6	4
21	31213	5	3
20	29892	5	3
19	24442	5	3
18	19091	5	3
17	17671	5	3
16	12221	5	3
15	10701	5	3
14	646	3	2
13	272	3	2
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 34	L base 10	L base 34
	Next > 10^20
73	74850890322309805847	20	13
72	49116020022002061194	20	13
71	40329654488445692304	20	13
70	36120528966982502163	20	13
69	13738892611629883731	20	13
68	13464966499466946431	20	13
67	4980354200024530894	19	13
66	3068265789875628603	19	13
65	66618580008581666	17	11
64	66387132523178366	17	11
63	63344575857544336	17	11
62	62703992029930726	17	11
61	57360531413506375	17	11
60	51914591419541915	17	11
59	46571130803117564	17	11
58	42805321512350824	17	11
57	41596743034769514	17	11
56	29974237873247992	17	11
55	26712276167221762	17	11
54	11727327672372711	17	11
53	Prime! 11376545454567311	17	11
52	7894167667614987	16	11
51	6173061111603716	16	11
50	3630457117540363	16	11
49	3033080770803303	16	11
48	43649088094634	14	9
47	9950190910599	13	9
46	9326196916239	13	9
45	5641401041465	13	9
44	4048267628404	13	9
43	43590509534	11	7
42	35793239753	11	7
41	30632523603	11	7
40	30268686203	11	7
39	28185658182	11	7
38	22835253822	11	7
37	18319091381	11	7
36	6447777446	10	7
35	5086996805	10	7
34	4601881064	10	7
33	525868525	9	6
32	31500513	8	5
31	29622692	8	5
30	8632368	7	5
29	8066608	7	5
28	7446447	7	5
27	5020205	7	5
26	2967692	7	5
25	38283	5	3
24	32123	5	3
23	31613	5	3
22	28482	5	3
21	27972	5	3
20	21812	5	3
19	Prime! 16061	5	3
18	Prime! 15551	5	3
17	9119	4	3
16	2552	4	3
15	595	3	2
14	525	3	2
13	33	2	1
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 35	L base 10	L base 35
	Next > 10^20
86	80804050955905040808	20	13
85	76992678711787629967	20	13
84	76505756233265750567	20	13
83	48005895800859850084	20	13
82	26359176200267195362	20	13
81	7794403740473044977	19	13
80	7775913126213195777	19	13
79	7736456939396546377	19	13
78	7675459513159545767	19	13
77	7458819033309188547	19	13
76	7377239767679327737	19	13
75	7360219995999120637	19	13
74	7062044826284402607	19	13
73	6386383582853836836	19	13
72	6187432844482347816	19	13
71	2192548599958452912	19	12
70	840796119911697048	18	12
69	801949761167949108	18	12
68	94935358285353949	17	11
67	94912815351821949	17	11
66	94506362726360549	17	11
65	94154052825045149	17	11
64	Prime! 75930888788803957	17	11
63	75138056765083157	17	11
62	75113827972831157	17	11
61	56584814841848565	17	11
60	56528122722182565	17	11
59	56120175257102165	17	11
58	40916991319961904	17	11
57	40543993339934504	17	11
56	Prime! 37964160106146973	17	11
55	Prime! 37589506860598573	17	11
54	21548685358684512	17	11
53	21175687378657112	17	11
52	18571625352617581	17	11
51	17731713731713771	17	11
50	17302023632020371	17	11
49	232131696131232	15	10
48	217030505030712	15	10
47	30869533596803	14	9
46	28165944956182	14	9
45	Prime! 9710780870179	13	9
44	9638309038369	13	9
43	8703990993078	13	9
42	2121358531212	13	8
41	2102654562012	13	8
40	69497279496	11	8
39	56028182065	11	7
38	55972827955	11	7
37	55964546955	11	7
36	34145054143	11	7
35	Prime! 33842924833	11	7
34	33834643833	11	7
33	23780308732	11	7
32	23772027732	11	7
31	12599199521	11	7
30	9166226619	10	7
29	26922962	8	5
28	Prime! 1881881	7	5
27	65556	5	4
26	63036	5	4
25	42524	5	3
24	34643	5	3
23	27672	5	3
22	21612	5	3
21	19791	5	3
20	14641	5	3
19	13731	5	3
18	3993	4	3
17	2662	4	3
16	1331	4	3
15	828	3	2
14	252	3	2
13	33	2	1
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Index Nr	Also palindromic in base 36 A250412	L base 10	L base 36
	Next > 10^20
98	89811756188165711898	20	13
97	89128718100181782198	20	13
96	68332722733722723386	20	13
95	40685060744706058604	20	13
94	21783718822881738712	20	13
93	5056422359532246505	19	13
92	2476507590957056742	19	12
91	854404185581404458	18	12
90	839256186681652938	18	12
89	116979806608979611	18	11
88	77305171417150377	17	11
87	70701803330810707	17	11
86	70649867676894607	17	11
85	70546180208164507	17	11
84	66934618481643966	17	11
83	57673510101537675	17	11
82	50813624942631805	17	11
81	46524937473942564	17	11
80	46421250005212464	17	11
79	13906815051860931	17	11
78	5804986116894085	16	11
77	389004000400983	15	10
76	361400848004163	15	10
75	343201454102343	15	10
74	85582866828558	14	9
73	67743488434776	14	9
72	32866755766823	14	9
71	28420977902482	14	9
70	25120399302152	14	9
69	3955010105593	13	9
68	2402398932042	13	8
67	1679755579761	13	8
66	73533033537	11	7
65	71904040917	11	7
64	66516061566	11	7
63	66394149366	11	7
62	61664946616	11	7
61	59552225595	11	7
60	56276967265	11	7
59	56102620165	11	7
58	54647974645	11	7
57	49931613994	11	7
56	44596069544	11	7
55	37579097573	11	7
54	37280408273	11	7
53	27958485972	11	7
52	22446164422	11	7
51	952343259	9	6
50	48655684	8	5
49	10066001	8	5
48	9488849	7	5
47	9242429	7	5
46	6950596	7	5
45	6918196	7	5
44	5927295	7	5
43	5182815	7	5
42	4306034	7	5
41	Prime! 3315133	7	5
40	1867681	7	5
39	1301031	7	4
38	987789	6	4
37	741147	6	4
36	159951	6	4
35	42224	5	3
34	37973	5	3
33	36063	5	3
32	33433	5	3
31	Prime! 30803	5	3
30	21112	5	3
29	19491	5	3
28	16861	5	3
27	12321	5	3
26	5115	4	3
25	2882	4	3
24	1441	4	3
23	1221	4	2
22	999	3	2
21	888	3	2
20	777	3	2
19	666	3	2
18	555	3	2
17	444	3	2
16	333	3	2
15	222	3	2
14	111	3	2
13	33	2	1
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

MISSING TABLES PLANNED FOR
CONSTRUCTION IN THE FUTURE

Index Nr	Also palindromic in base 60 A262069	L base 10	L base 60
	Next >10^20
88	19260605633650606291	20	11
87	19109139233293190191	20	11
86	19108306011060380191	20	11
85	12953949300394935921	20	11
84	1059511493941159501	19	11
83	1008860210120688001	19	11
82	111705028820507111	18	10
81	96791647174619769	17	10
80	94855661216655849	17	10
79	94812756665721849	17	10
78	90820011311002809	17	10
77	86756027772065768	17	10
76	84686895859868648	17	10
75	78698827572889687	17	10
74	70632865556823607	17	10
73	62576136663167526	17	10
72	44454350005345444	17	10
71	40448567076584404	17	10
70	26334850305843362	17	10
69	18278121412187281	17	10
68	18235216861253281	17	10
67	6140607337060416	16	9
66	5979490660949795	16	9
65	4056041771406504	16	9
64	4041670880761404	16	9
63	2114962552694112	16	9
62	2114927447294112	16	9
61	1997507557057991	16	9
60	1982186226812891	16	9
59	1927217227127291	16	9
58	1912846336482191	16	9
57	1021449441201	13	7
56	872376673278	12	7
55	872322223278	12	7
54	2230660322	10	6
53	1486446841	10	6
52	608363806	9	5
51	607272706	9	5
50	606181606	9	5
49	605090506	9	5
48	603070306	9	5
47	589616985	9	5
46	588525885	9	5
45	587434785	9	5
44	586343685	9	5
43	585252585	9	5
42	584161485	9	5
41	451929154	9	5
40	450838054	9	5
39	Prime! 301969103	9	5
38	155505551	9	5
37	155343551	9	5
36	154414451	9	5
35	Prime! 154252451	9	5
34	Prime! 153323351	9	5
33	153161351	9	5
32	152232251	9	5
31	152070251	9	5
30	151141151	9	5
29	150050051	9	5
28	28933982	8	5
27	26233262	8	5
26	14033041	8	5
25	11166111	8	4
24	8372738	7	4
23	2796972	7	4
22	148841	6	3
21	113311	6	3
20	57375	5	3
19	57075	5	3
18	55755	5	3
17	55455	5	3
16	55155	5	3
15	55	2	1
14	44	2	1
13	33	2	1
12	22	2	1
11	Prime! 11	2	1
10	9	1	1
9	8	1	1
8	Prime! 7	1	1
7	6	1	1
6	Prime! 5	1	1
5	4	1	1
4	Prime! 3	1	1
3	Prime! 2	1	1
2	1	1	1
1	0	1	1

Base 2

Messages

Palindromes in bases 2 and 10.
The main source for this table comes from the following weblink.
Binary/Decimal Palindromes by Charlton Harrison (email) from Austin, Texas.
See also Sloane's sequences A007632 and A046472.

" I just finished writing a distributed client/server program for finding these numbers, and I currently
have it running on 4 different machines at the same time and I'm finding them A LOT faster. That's how
I was able to come up with those new ones. I'd say there are more to come in the near future, too."

[ December 1, 2001 ]
Charlton Harrison once found this record binary

decimal palindrome
110 0010111100 0010101010 1101000011 1010000010
0000101110 0001011010 1010100001 1110100011
7475703079870789703075747
The binary string contains 83 digits !

[ April 11, 2003 ]
Dw (email) wrote me the following :

"Using a backtracking solver, I have found larger numbers.
The first of these, which is the next after the one mentioned above, is
50824513851188115831542805 (86 bit, 3*5*11*11*17*17*83*11974799*97488286319).
There are no other 86 bit double palindromes.

I also have found two 89 bit double palindromes, but I am not sure if they
are the next ones. There may be some lower ones in 89 bit (haven't searched
that space completely yet) or in 87 bit that I haven't found.
These numbers are
532079161251434152161970235 (5*29*85839676103*42748430836381)
and
552963956270141072659369255 (5*7*7*71*441607*71984077228507867)
As can be seen by their factor representation, they are all composite."

50824513851188115831542805 {26}
10101000001010100000100110101010101001100000000110010101010101100100000101010000010101 {86}

532079161251434152161970235 {27}
11011100000100000001001010010000011001110101010101110011000001001010010000000100000111011 {89}

552963956270141072659369255 {27}
11100100101100110101011000010001001111100100100100111110010001000011010101100110100100111 {89}

[ April 13, 2003 ]
Dw (email) found four new ones including the 6^th double palindromic prime :

"They are, in opposite sorted order:
138758321383797383123857831 (87 bit, composite, the only 87 bit double palindrome)
390714505091666190505417093 (89 bit, prime)
351095331428353824133590153 (89 bit, composite)
795280629691202196926082597 (90 bit, composite, not sure if this is the next one)."

When asking Dw for an explanation or description in a few words
what he meant by 'Using a backtracking solver' he replied :

"A backtracking solver is one that solves a problem made up of smaller
problems by trying every one except if it knows its earlier guesses make all
later ones depending on them impossible.

For instance, if you're in a maze and know that all corridors with green
walls eventually lead to a dead end, you can turn around as soon as you find
such a wall (backtrack) if you're trying to find the exit.

The smaller problem is avoiding a dead end, and the larger one is
finding the exit.

If you want the details:

My general strategy goes that to find a double palindromic number, the
solution to its palindromic decimal representation minus its binary
representation must be zero (since they are equal).

Furthermore, you can write a decimal palindrome like 101 * a + 10 * b, where
a and b are digits. The same can be done for binary, and you end up with a
giant (linear diophantine) equation of positive decimal and negative binary factors.

The factors can then be solved, one at a time, using the extended euclidean
algorithm. These are the smaller problems.

I also have a table of maximum and minimum values for each step. That way, if
it's impossible for the binary factors left to subtract enough from the
decimal factors to get zero (or the other way around), the solver backtracks."

[ April 13, 2003 ]
Dw once found this record binary

decimal palindrome
1010010001 1101011100 1110010101 0010100001 0100000010 1000010100 1010100111 0011101011 1000100101
795280629691202196926082597
The binary string contains 90 digits !
The decimal string contains 27 digits !

138758321383797383123857831 {27}
111001011000111001101111010110010111011100111001110111010011010111101100111000110100111 {87}

351095331428353824133590153 {27}
10010001001101011010101000000110111100000100000100000111101100000010101011010110010001001 {89}

390714505091666190505417093 {27}
10100001100110001000000111100001100011000111011100011000110000111100000010001100110000101 {89}

795280629691202196926082597 {27}
101001000111010111001110010101001010000101000000101000010100101010011100111010111000100101 {90}

[ May 21, 2003 ]
Dw (email) found a new Binary/Decimal Palindrome :

"I have been trying to find a polynomial time (growth of time needed is a
polynomial of number of bits) algorithm for finding double palindromes of
base 2 and 10. I haven't succeeded yet (my backtracking solver being
exponential), but I have found some interesting things.

For one, to find double palindromes in base 2 and 8 is very simple. Each base 8
digit maps to three bits. Therefore, every double palindrome must consist
of digits who themselves are double palindromes.

For instance, 757 as well as 575 is double palindromic. (These values are 495
and 381 in decimal respectively).
5 maps to 101 in binary, and 7 to 111 in binary.

I have found 1609061098335005338901609061 (91 bits composite),
and this is the only 91 bit one. No 92 bit double palindrome exists, and
93 bits seems to require several days of searching; therefore I'm trying to
find a polynomial time algorithm as mentioned above.

Another approach could be to create a networked version (to do the search on
multiple computers), but I haven't done that yet."

[ May 21, 2003 ]
Dw once found this record binary

decimal palindrome
1 0100110010 1111101111 1100001110 1100100000
0010001000 0000100110 1110000111 1110111110 1001100101
1609061098335005338901609061
The binary palindrome contains 91 digits !
The decimal string contains 28 digits !

1609061098335005338901609061 {28}
1010011001011111011111100001110110010000000100010000000100110111000011111101111101001100101 {91}

[ June 12, 2003 ]
Dw (email) found new Binary/Decimal Palindromes :

"I rewrote my program to use another strategy at finding the numbers, and this
let me search somewhat faster. As a result, I have found binary/decimal
palindromes up to 102 bits -- broke the 100 bit barrier so to speak.

These are:

None at 92 or 93 bits.
17869806142184248124160896871 (94 bits)
19756291244127372144219265791 (94 bits)
30000258151173237115185200003 (95 bits)
30658464822225352222846485603 (95 bits)
56532345659072227095654323565 (96 bits)
None at 97 or 98 bits.
378059787464677776464787950873 (99 bits)
1115792035060833380605302975111 (100 bits)
None at 101 bits.
3390741646331381831336461470933 (102 bits)

There may be higher ones at 102 bits; I haven't completed the search there."

17869806142184248124160896871 {29}
1110011011110110001110101001000001000000000011001100000000001000001001010111000110111101100111 {94}

19756291244127372144219265791 {29}
1111111101011000000101011001100101101101100001111000011011011010011001101010000001101011111111 {94}

30000258151173237115185200003 {29}
11000001110111110100001110001010010000110100011011000101100001001010001110000101111101110000011 {95}

30658464822225352222846485603 {29}
11000110001000000010110011101000100010000101111111110100001000100010111001101000000010001100011 {95}

56532345659072227095654323565 {29}
101101101010101001110101110101101111011010100000000001010110111101101011101011100101010101101101 {96}

378059787464677776464787950873 {30}
100110001011001001110111010000000001110111000111010111000111011100000000010111011100100110100011001 {99}

1115792035060833380605302975111 {31}
1110000101010101000110001001111111101011111110110110110111111101011111111001000110001010101010000111 {100}

3390741646331381831336461470933 {31}
101010110011000001001111000000100001000111101001011110100101111000100001000000111100100000110011010101 {102}

[ June 17, 2003 ]
Dw (email) adds :

" There are no numbers for 103 bits."

[ Note : In fact there is one! See index number 97. PDG ]

[ June 17, 2003 ]
Dw once found this record binary

decimal palindrome
10 1010110011 0000010011 1100000010 0001000111 1010010111
1010010111 1000100001 0000001111 0010000011 0011010101
3390741646331381831336461470933
The binary palindrome contains 102 digits !
The decimal string contains 31 digits !

Binary/Decimal Palindromes by Charlton Harrison (email) : the longest list in existence ?

[ September 30, 2015 ]
Three more stunning numbers could be retrieved from Sloane's OEIS database.
See index numbers 124, 125 & 126.

[ September 30, 2015 ]
A former record binary

decimal palindrome
100110011011011101000001000010000011000111001011100111100011101000
00101110001111001110100111000110000010000100000101110110110011001
1634587141488515712882175158841417854361
The binary palindrome contains 131 digits !
The decimal string contains 40 digits !

[ March 8, 2020 ]
Many more numbers could be retrieved from Sloane's OEIS database.
See index numbers up to 147. The record dates from the end of 2015.

[ December 30, 2015 ]
The current record binary

decimal palindrome
Search team : Robert G. Wilson v, Charlton Harrison, Ilya Nikulshin & Andrey Astrelin
11010001010011101000000001001100010000000010110001011110100100101011100110101
0101100111010100100101111010001101000000001000110010000000010111001010001011
9335388324586156026843333486206516854238835339
The binary palindrome contains 153 digits !
The decimal string contains 46 digits !

Sources Revealed

Binary/Decimal Palindromes by Charlton Harrison (email) : the longest list in existence ?

Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :

Neil Sloane's Integer Sequences

I sampled the following base X palindromic numbers sequences from the table :
%N Binary expansion is palindromic. under A006995 -- Sum of digits A043261

%N Palindromes in base 3 (written in base 10). under A014190 -- Sum of digits A043262

%N Palindromes in base 4 (written in base 10). under A014192 -- Sum of digits A043263

%N Palindromic in base 5. under A029952 -- Sum of digits A043264

%N Palindromic in base 6. under A029953 -- Sum of digits A043265

%N Palindromic in base 7. under A029954 -- Sum of digits A043266

%N Palindromic in base 8. under A029803 -- Sum of digits A043267

%N Palindromic in base 9. under A029955 -- Sum of digits A043268

%N Palindromes. under A002113 -- Sum of digits A043269

%N Palindromic in base 11. under A029956 -- Sum of digits A043270

%N Palindromic in base 12. under A029957 -- Sum of digits A043271

%N Palindromic in base 13. under A029958 -- Sum of digits A043272

%N Palindromic in base 14. under A029959 -- Sum of digits A043273

%N Palindromic in base 15. under A029960 -- Sum of digits A043274

%N Palindromic in base 16. under A029730 -- Sum of digits A043275

%N Palindromic in bases 2 and 3. under A060792.

%N Palindromic in bases 2 and 10. under A007632.

%N Palindromic in bases 3 and 10. under A007633.

%N Palindromic in bases 4 and 10. under A029961.

%N Palindromic in bases 5 and 10. under A029962.

%N Palindromic in bases 6 and 10. under A029963.

%N Palindromic in bases 7 and 10. under A029964.

%N Palindromic in base 8 and base 10. under A029804.

%N Palindromic in bases 9 and 10. under A029965.

%N Palindromic in bases 11 and 10. under A029966.

%N Palindromic in bases 12 and 10. under A029967.

%N Palindromic in bases 13 and 10. under A029968.

%N Palindromic in bases 14 and 10. under A029969.

%N Palindromic in bases 15 and 10. under A029970.

%N Square in base 2 is a palindrome. under A003166.

%N Squares which are palindromes in base 2. under A029983.

%N n^2 is palindromic in base 3. under A029984.

%N Squares which are palindromic in base 3. under A029985.

%N n^2 is palindromic in base 4. under A029986.

%N Squares which are palindromic in base 4. under A029987.

%N n^2 is palindromic in base 5. under A029988.

%N Squares which are palindromic in base 5. under A029989.

%N n^2 is palindromic in base 6. under A029990.

%N Squares which are palindromic in base 6. under A029991.

%N n^2 is palindromic in base 7. under A029992.

%N Squares which are palindromic in base 7. under A029993.

%N n^2 is palindromic in base 8. under A029805.

%N n in base 8 is a palindromic square. under A029806.

%N n^2 is palindromic in base 9. under A029994.

%N Squares which are palindromic in base 9. under A029995.

%N Square is a palindrome. under A002778.

%N Palindromic Squares. under A002779.

%N n^2 is palindromic in base 11. under A029996.

%N Squares which are palindromic in base 11. under A029997.

%N n^2 is palindromic in base 12. under A029737.

%N Squares which are palindromic in base 12. under A029738.

%N n^2 is palindromic in base 13. under A029998.

%N Squares which are palindromic in base 13. under A029999.

%N n^2 is palindromic in base 14. under A030072.

%N Squares which are palindromes in base 14. under A030074.

%N n^2 is palindromic in base 15. under A030073.

%N Squares which are palindromes in base 15. under A030075.

%N n^2 is palindromic in base 16. under A029733.

%N Palindromic squares in base 16. under A029734.

%N n^3 is palindromic in base 4. under A046231.

%N Cubes which are palindromes in base 4. under A046232.

%N n^3 is palindromic in base 5. under A046233.

%N Cubes which are palindromes in base 5. under A046234.

%N n^3 is palindromic in base 6. under A046235.

%N Cubes which are palindromes in base 6. under A046236.

%N n^3 is palindromic in base 7. under A046237.

%N Cubes which are palindromes in base 7. under A046238.

%N n^3 is palindromic in base 8. under A046239.

%N Cubes which are palindromes in base 8. under A046240.

%N n^3 is palindromic in base 9. under A046241.

%N Cubes which are palindromes in base 9. under A046242.

%N Cube is a palindrome. under A002780.

%N Palindromic cubes. under A002781.

%N n^3 is palindromic in base 11. under A046243.

%N Cubes which are palindromes in base 11. under A046244.

%N n^3 is palindromic in base 12. under A046245.

%N Cubes which are palindromes in base 12. under A046246.

%N n^3 is palindromic in base 13. under A046247.

%N Cubes which are palindromes in base 13. under A046248.

%N n^3 is palindromic in base 14. under A046249.

%N Cubes which are palindromes in base 14. under A046250.

%N n^3 is palindromic in base 15. under A046251.

%N Cubes which are palindromes in base 15. under A046252.

%N n^3 is palindromic in base 16. under A029735.

%N Cubes which are palindromes in base 16. under A029736.

%N Palindromic primes in base 2. under A016041.

%N Palindromic primes in base 3. under A029971.

%N Palindromic primes in base 4. under A029972.

%N Palindromic primes in base 5. under A029973.

%N Palindromic primes in base 6. under A029974.

%N Palindromic primes in base 7. under A029975.

%N Palindromic primes in base 8. under A029976.

%N Octal palindromes which are also primes. under A006341.

%N Palindromic primes in base 9. under A029977.

%N Palindromic primes. under A002385.

%N Palindromic primes in base 11. under A029978.

%N Palindromic primes in base 12. under A029979.

%N Palindromic primes in base 13. under A029980.

%N Palindromic primes in base 14. under A029981.

%N Palindromic primes in base 15. under A029982.

%N Palindromic primes in base 16. under A029732.

%N Palindromic primes in base 10 and base 2. under A046472.

%N Palindromic primes in base 10 and base 3. under A046473.

%N Palindromic primes in base 10 and base 4. under A046474.

%N Palindromic primes in base 10 and base 6. under A046475.

%N Palindromic primes in base 10 and base 7. under A046476.

%N Palindromic primes in base 10 and base 8. under A046477.

%N Palindromic primes in base 10 and base 9. under A046478.

%N Palindromic primes. under A002385.

%N Palindromic primes in base 10 and base 11. under A046479.

%N Palindromic primes in base 10 and base 12. under A046480.

%N Palindromic primes in base 10 and base 13. under A046481.

%N Palindromic primes in base 10 and base 14. under A046482.

%N Palindromic primes in base 10 and base 15. under A046483.

%N Palindromic primes in base 10 and base 16. under A046484.

%N Palindromic primes in bases 2 and 4. under A056130.

%N Palindromic primes in bases 2 and 8. under A056145.

%N Palindromic primes in bases 4 and 8. under A056146.

%N Not palindromic in any base from 2 to n-2. under A016038.

%N Smallest palindrome greater than n in bases n and n+1. under A048268.

%N First palindrome greater than n+2 in bases n+2 and n. under A048269.

%N The first non-trivial (k>n+2) palindromic prime in both bases n and n+2. under A057199.

%N Symmetric bit strings (bit-reverse palindromes),

including as many leading as trailing zeros. under A057890.

Click here to view some of the author's [P. De Geest] entries to the table.
Click here to view some entries to the table about palindromes.

More Integer Sequences from Sloane's OEIS database

A043001 n-th base 3 palindrome that starts with 1. - Clark Kimberling

A043002 n-th base 3 palindrome that starts with 2. - Clark Kimberling

A043003 n-th base 4 palindrome that starts with 1. - Clark Kimberling

A043004 n-th base 4 palindrome that starts with 2. - Clark Kimberling

A043005 n-th base 4 palindrome that starts with 3. - Clark Kimberling

A043006 n-th base 5 palindrome that starts with 1. - Clark Kimberling

A043007 n-th base 5 palindrome that starts with 2. - Clark Kimberling

A043008 n-th base 5 palindrome that starts with 3. - Clark Kimberling

A043009 n-th base 5 palindrome that starts with 4. - Clark Kimberling

A043010 n-th base 6 palindrome that starts with 1. - Clark Kimberling

A043011 n-th base 6 palindrome that starts with 2. - Clark Kimberling

A043012 n-th base 6 palindrome that starts with 3. - Clark Kimberling

A043013 n-th base 6 palindrome that starts with 4. - Clark Kimberling

A043014 n-th base 6 palindrome that starts with 5. - Clark Kimberling

A043015 n-th base 7 palindrome that starts with 1. - Clark Kimberling

A043016 n-th base 7 palindrome that starts with 2. - Clark Kimberling

A043017 n-th base 7 palindrome that starts with 3. - Clark Kimberling

A043018 n-th base 7 palindrome that starts with 4. - Clark Kimberling

A043019 n-th base 7 palindrome that starts with 5. - Clark Kimberling

A043020 n-th base 7 palindrome that starts with 6. - Clark Kimberling

A043021 n-th base 8 palindrome that starts with 1. - Clark Kimberling

A043022 n-th base 8 palindrome that starts with 2. - Clark Kimberling

A043023 n-th base 8 palindrome that starts with 3. - Clark Kimberling

A043024 n-th base 8 palindrome that starts with 4. - Clark Kimberling

A043025 n-th base 8 palindrome that starts with 5. - Clark Kimberling

A043026 n-th base 8 palindrome that starts with 6. - Clark Kimberling

A043027 n-th base 8 palindrome that starts with 7. - Clark Kimberling

A043028 n-th base 9 palindrome that starts with 1. - Clark Kimberling

A043029 n-th base 9 palindrome that starts with 2. - Clark Kimberling

A043030 n-th base 9 palindrome that starts with 3. - Clark Kimberling

A043031 n-th base 9 palindrome that starts with 4. - Clark Kimberling

A043032 n-th base 9 palindrome that starts with 5. - Clark Kimberling

A043033 n-th base 9 palindrome that starts with 6. - Clark Kimberling

A043034 n-th base 9 palindrome that starts with 7. - Clark Kimberling

A043035 n-th base 9 palindrome that starts with 8. - Clark Kimberling

A043036 n-th base 10 palindrome that starts with 1. - Clark Kimberling

A043037 n-th base 10 palindrome that starts with 2. - Clark Kimberling

A043038 n-th base 10 palindrome that starts with 3. - Clark Kimberling

A043039 n-th base 10 palindrome that starts with 4. - Clark Kimberling

A043040 n-th base 10 palindrome that starts with 5. - Clark Kimberling

A043041 n-th base 10 palindrome that starts with 6. - Clark Kimberling

A043042 n-th base 10 palindrome that starts with 7. - Clark Kimberling

A043043 n-th base 10 palindrome that starts with 8. - Clark Kimberling

A043044 n-th base 10 palindrome that starts with 9. - Clark Kimberling

A043045 a(n)=(s(n)+2)/3, where s(n)=n-th base 3 palindrome that starts with 1. - Clark Kimberling

A043046 a(n)=(s(n)+1)/3, where s(n)=n-th base 3 palindrome that starts with 2. - Clark Kimberling

A043047 a(n)=(s(n)+3)/4, where s(n)=n-th base 4 palindrome that starts with 1. - Clark Kimberling

A043048 a(n)=(s(n)+2)/4, where s(n)=n-th base 4 palindrome that starts with 2. - Clark Kimberling

A043049 a(n)=(s(n)+1)/4, where s(n)=n-th base 4 palindrome that starts with 3. - Clark Kimberling

A043050 a(n)=(s(n)+4)/5, where s(n)=n-th base 5 palindrome that starts with 1. - Clark Kimberling

A043051 a(n)=(s(n)+3)/5, where s(n)=n-th base 5 palindrome that starts with 2. - Clark Kimberling

A043052 a(n)=(s(n)+2)/5, where s(n)=n-th base 5 palindrome that starts with 3. - Clark Kimberling

A043053 a(n)=(s(n)+1)/5, where s(n)=n-th base 5 palindrome that starts with 4. - Clark Kimberling

A043054 a(n)=(s(n)+5)/6, where s(n)=n-th base 6 palindrome that starts with 1. - Clark Kimberling

A043055 a(n)=(s(n)+4)/6, where s(n)=n-th base 6 palindrome that starts with 2. - Clark Kimberling

A043056 a(n)=(s(n)+3)/6, where s(n)=n-th base 6 palindrome that starts with 3. - Clark Kimberling

A043057 a(n)=(s(n)+2)/6, where s(n)=n-th base 6 palindrome that starts with 4. - Clark Kimberling

A043058 a(n)=(s(n)+1)/6, where s(n)=n-th base 6 palindrome that starts with 5. - Clark Kimberling

A043059 a(n)=(s(n)+6)/7, where s(n)=n-th base 7 palindrome that starts with 1. - Clark Kimberling

A043060 a(n)=(s(n)+5)/7, where s(n)=n-th base 7 palindrome that starts with 2. - Clark Kimberling

A043061 a(n)=(s(n)+4)/7, where s(n)=n-th base 7 palindrome that starts with 3. - Clark Kimberling

A043062 a(n)=(s(n)+3)/7, where s(n)=n-th base 7 palindrome that starts with 4. - Clark Kimberling

A043063 a(n)=(s(n)+2)/7, where s(n)=n-th base 7 palindrome that starts with 5. - Clark Kimberling

A043064 a(n)=(s(n)+1)/7, where s(n)=n-th base 7 palindrome that starts with 6. - Clark Kimberling

A043065 a(n)=(s(n)+7)/8, where s(n)=n-th base 8 palindrome that starts with 1. - Clark Kimberling

A043066 a(n)=(s(n)+6)/8, where s(n)=n-th base 8 palindrome that starts with 2. - Clark Kimberling

A043067 a(n)=(s(n)+5)/8, where s(n)=n-th base 8 palindrome that starts with 3. - Clark Kimberling

A043068 a(n)=(s(n)+4)/8, where s(n)=n-th base 8 palindrome that starts with 4. - Clark Kimberling

A043069 a(n)=(s(n)+3)/8, where s(n)=n-th base 8 palindrome that starts with 5. - Clark Kimberling

A043070 a(n)=(s(n)+2)/8, where s(n)=n-th base 8 palindrome that starts with 6. - Clark Kimberling

A043071 a(n)=(s(n)+1)/8, where s(n)=n-th base 8 palindrome that starts with 7. - Clark Kimberling

A043072 a(n)=(s(n)+8)/9, where s(n)=n-th base 9 palindrome that starts with 1. - Clark Kimberling

A043073 a(n)=(s(n)+7)/9, where s(n)=n-th base 9 palindrome that starts with 2. - Clark Kimberling

A043074 a(n)=(s(n)+6)/9, where s(n)=n-th base 9 palindrome that starts with 3. - Clark Kimberling

A043075 a(n)=(s(n)+5)/9, where s(n)=n-th base 9 palindrome that starts with 4. - Clark Kimberling

A043076 a(n)=(s(n)+4)/9, where s(n)=n-th base 9 palindrome that starts with 5. - Clark Kimberling

A043077 a(n)=(s(n)+3)/9, where s(n)=n-th base 9 palindrome that starts with 6. - Clark Kimberling

A043078 a(n)=(s(n)+2)/9, where s(n)=n-th base 9 palindrome that starts with 7. - Clark Kimberling

A043079 a(n)=(s(n)+1)/9, where s(n)=n-th base 9 palindrome that starts with 8. - Clark Kimberling

A043080 a(n)=(s(n)+9)/10, where s(n)=n-th base 10 palindrome that starts with 1. - Clark Kimberling

A043081 a(n)=(s(n)+8)/10, where s(n)=n-th base 10 palindrome that starts with 2. - Clark Kimberling

A043082 a(n)=(s(n)+7)/10, where s(n)=n-th base 10 palindrome that starts with 3. - Clark Kimberling

A043083 a(n)=(s(n)+6)/10, where s(n)=n-th base 10 palindrome that starts with 4. - Clark Kimberling

A043084 a(n)=(s(n)+5)/10, where s(n)=n-th base 10 palindrome that starts with 5. - Clark Kimberling

A043085 a(n)=(s(n)+4)/10, where s(n)=n-th base 10 palindrome that starts with 6. - Clark Kimberling

A043086 a(n)=(s(n)+3)/10, where s(n)=n-th base 10 palindrome that starts with 7. - Clark Kimberling

A043087 a(n)=(s(n)+2)/10, where s(n)=n-th base 10 palindrome that starts with 8. - Clark Kimberling

A043088 a(n)=(s(n)+1)/10, where s(n)=n-th base 10 palindrome that starts with 9. - Clark Kimberling

A016038 Strictly non-palindromic numbers: n is not palindromic in any base b with 2 <= b <= n-2. - N. J. A. Sloane.

A100563 Number of bases less than sqrt(n) in which n is a palindrome. - Gordon Robert Hamilton

Contributions

Kevin Brown informed me that he has more info about tetrahedral palindromes in other base representations.
Link to his article :
On General Palindromic Numbers

Alain Bex (email) sent me the first palindromic squares in base 12 - go to topic.

Dw (email) found several binary/decimal palindromes of record lengths - go to topic.

Richard Gosiorovsky (email)
Also Palindromic in Base 16 (OEIS A029731)
[ do 7-8/3/2024 7:33 ]

Dear Mr. De Geest,

I would like to ask you for updating the table re. numbers that are palindromic in bases 10 and 16.
I did some progress on it, and found 51 new members of the sequence. See indices 84 up to 134.
Full list of new members is in the text file in the attachment.

Thank you,

Richard Gosiorovsky, Bratislava

When I asked Richard how he achieved his results he replied:

I was inspired by Eshed Schacham's nice article:
"Finding Binary & Decimal Palindromes"

The method is useful for powers of two bases (2,4,8,16).
For now I do not plan other bases. It took me 3 days of
experimenting (programming) and 2 days of running (CPU time).

If you are interested in I am sending you my piece of code
in C language (palindrom.c) with external function in assembler
allowing multiply two 64-bit integers into 128-bit value.

Now I must go on with my real job, programming of course :)

Richard

//
//   Looking for Numbers that are palindromic in bases 10 and 16 simultaneously
//

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

#define ull unsigned long long  // 64-bit integer

extern ull mul128(ull *c, ull a, ull b);  // mul128.asm, see here:

// mul128 PROC
// mov rax, rdx              ; rdx - 2nd argument,  r8 - 3rd argument
// mul r8                    ; multiply rax * r8 -> result = 128-bit rdx:rax
// mov qword ptr [rcx], rdx  ; rcx - 1st argument
// ret                       ; return rax    
// mul128 ENDP

inline ull reverse(ull x) { ull q, y=0;  while(x) { q=x/10;  y=10*(y-q)+x;  x=q; }  return y; }

inline int is_palind_128(ull h64, ull l64, int sh1, int sh2)
 {
   while(sh1 >= 0 ) { if ((h64>>sh1 & 0xf) != (l64>>sh2 & 0xf)) return 0;   sh1-=4;  sh2+=4; }  sh1 = 60;  
   while(sh1 > sh2) { if ((l64>>sh1 & 0xf) != (l64>>sh2 & 0xf)) return 0;   sh1-=4;  sh2+=4; }  // here we test only in lower 64-bit
   return 1;
 }

//           012345678901234567890
#define FROM 10000000000000LL
#define UPTO 100000000000000LL
#define M4   10000000000LL
#define M8   1000000
#define M12  100

int main(int argc, char *argv[])
 {
   int sh=-999, k=0;
   ull h64, l64;  // upper & lower 64-bit of palindrome

   for(ull i=FROM; i<UPTO; i++)  // i - half of palindrome
    {
      if (i%1000000000==0) printf(" %lld mld.   %d sec.  %16llx\r", i/1000000000, clock()/1000, h64);

      l64 = mul128(&h64, i/10, UPTO) + reverse(i);  // create palindrome:  i - for even symmetry,  i/10 - for odd symmetry

      if (sh==-999) { sh=60;   while((h64>>sh & 0xf)==0) sh-=4; }  // find initial shift for leading hex digit
      if (h64>>(sh+4) & 0xf) sh+=4;  // hex digit overflow happened -> increase shift

      if (i % M4 == 0) if ((h64 >>(sh   ) & 0x000f) != (l64 & 0x000f)) { i+=M4 -1;  continue; } // skip this foursome of decimal digits
      if (i % M8 == 0) if ((h64 >>(sh- 8) & 0x00f0) != (l64 & 0x00f0)) { i+=M8 -1;  continue; }
      if (i % M12== 0) if ((h64 >>(sh-16) & 0x0f00) != (l64 & 0x0f00)) { i+=M12-1;  continue; }

      // 3*4 - first/last 3 hex digits was already tested by 3 upper conditions
      if (is_palind_128(h64, l64, sh-3*4, 3*4)) printf(" %4d.  %lld  %8llx:%016llx  %d sec.\n", ++k, i, h64, l64, clock()/1000);
    }

   printf(" total time = %d sec.\t\t\t\n", clock()/1000);   getchar();
 }

Eshed Schacham's article can be found following this link:
https://ashdnazg.github.io/articles/22/Finding-Really-Big-Palindromes
As a software developer he also made public his .c code he wrote for this topic and explains the algorithm in great depth.

To my surprise he found 35 new decimal palindromes that are also palindromic in base 2 or binary.
I added them forthwith to my webpage. Please refer to indices 148 up to 183 in the very first
scrolltable of this very page. Impressive if you consider their record lengths.

Richard Gosiorovsky (email)
Dual-base Palindromes
[ do 2/5/2024 6:02 ]

Hi Patrick,

I am sending you in the attachment several
new records for dual-base palindromes:

base 10 & 3:    4 new records → From [71] to [74]
base 10 & 4:   35 new records → From [65] to [99]
base 10 & 5:  100 new records → From [84] to [183]
base 10 & 6:    9 new records → From [110] to [118]
base 10 & 7:    8 new records → From [74] to [81]
base 10 & 8:   43 new records → From [89] to [131]
base 10 & 9:    5 new records → From [71] to [75]
base 10 & 16:   9 new records → From [135] to [143]

Thank you for this interesting entertainment.

For bases 10 & 4, 10 & 8 and 10 & 16 I used practically the same method as I mentioned earlier.
For base pair 10 & 5 I used very similar method, main difference is that solutions don't fit into
128-bit (it prunes much faster) so I rewrite the code using GMP library (GNU multiple precision).

For the rest of base pairs I used optimized brute force method, where I generate all possible
palindromes in one base and check it in another one. In cases where one base is power of 2
it is pretty straightforward (just bits comparison).

In all cases (except 10 & 5) I employ possibility of Intel processor to multiply two 64-bit integers
into 128-bit value (rdx:rax) and division of this 128-bit value into quotient and remainder
(instructions mul, div).

Richard

Richard Gosiorovsky (email)
Dual-base Palindromes (bases 10 & 5)
[ do 5/8/2024 16:44 ]

Hi Patrick, Hi Eshed,

I am here again, I would like to ask you for updating dual-base
palindrome sequence A029962 (bases 10 & 5), where I found 52 new
members (in the attachement). I improved algorithm a bit, but it
is still far from optimal. Changing bases to 10 & 2 I can not
achieve Eshed's records at all. Basic idea remains the same.

Richard

PS: For better understanding I am sending the source code too
(it uses GMP - GNU multiple precision library)

/*
    Looking for numbers simultaneously palindromic in bases 10 and 5 
*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

#include "gmp.h"

#define ODD 1   // 0 - even symmetry  1 - odd symmetry

#define N 24    
#define M (2*N-1)  // length of palindrome

mpz_t tmp, aux;
mpz_t D[128], P[128];  // pre-computed constants: D[i] = 10^i,  P[i] = 5^i
mpz_t e[128], h[128];  // e[] - end of palindrome,  h[] - beginning of palindrome

int d[128], m1, m2;  // 5^m = divisor for leading digit
char s[256], s1[256], s2[256];

int ispalind(char *s, int n) { for(int i=0; i<n/2; i++) if (s[i] != s[n-i-1]) return 0;  return 1; }

void init_m1(mpz_t x) { m1 = M;   do { m1++;  mpz_fdiv_q(aux, x, P[m1]); } while (mpz_cmp_ui(aux, 5) >= 0); }
void init_m2(mpz_t x) { m2 = M;   do { m2++;  mpz_fdiv_q(aux, x, P[m2]); } while (mpz_cmp_ui(aux, 5) >= 0); }

int get_digit1(mpz_t x, int i)  // get i-th leading digit of x in base 5
 {
   mpz_fdiv_q(aux, x, P[m1]); 

   if (mpz_cmp_ui(aux, 5) >=0) m1++; 
   if (mpz_cmp_ui(aux, 0) <=0) m1--; 

   mpz_fdiv_q(aux, x, P[m1-i]);
   return mpz_fdiv_ui(aux, 5);
 }

int get_digit2(mpz_t x, int i)  // get i-th leading digit of x in base 5
 {
   mpz_fdiv_q(aux, x, P[m2]); 

   if (mpz_cmp_ui(aux, 5) >=0) m2++; 
   if (mpz_cmp_ui(aux, 0) <=0) m2--; 

   mpz_fdiv_q(aux, x, P[m2-i]);
   return mpz_fdiv_ui(aux, 5);
 }

void recur(int w)
 {
   if (w==6) { for(int i=0; i<6; i++) printf("%d", d[i]);  printf("  %d\"\r", clock()/1000); }

   if (w==N) 
    {
      mpz_add(tmp, h[N-1], (ODD==0)?e[N-1]:e[N-2]);
      mpz_get_str(s, 5, tmp);
      if (ispalind(s, strlen(s))) 
       { 
         for(int i=0; i<N; i++) printf("%d", d[i]);  
         printf("  %d  %d sec.\n", ODD, clock()/1000); 
       }
      return;
    }

   for(d[w]=0; d[w]<=9; d[w]++)
    {
      mpz_mul_ui(tmp, D[w], d[w]);        mpz_add(e[w], e[w-1], tmp);
      mpz_mul_ui(tmp, D[M-w-ODD], d[w]);  mpz_add(h[w], h[w-1], tmp);

      mpz_fdiv_q(tmp, e[w], P[w]);
      int f = mpz_fdiv_ui(tmp, 5); 
                                      
      mpz_add(tmp, h[w], D[M-w-ODD]); 

      if (f==get_digit1(h[w], w) || f==get_digit2(tmp, w)) recur(w+1);
    }
 }

int main()
 {
   printf("\n N = %d   ODD = %d\n\n", N, ODD);

   mpz_init(tmp);   mpz_init(aux); 
   for(int i=1; i<128; i++) { mpz_init(D[i]);  mpz_init(P[i]);  mpz_init(e[i]);  mpz_init(h[i]); }

   mpz_set_ui(D[0], 1);   for(int i=1; i<128; i++) mpz_mul_ui(D[i], D[i-1], 10); 
   mpz_set_ui(P[0], 1);   for(int i=1; i<128; i++) mpz_mul_ui(P[i], P[i-1], 5); 

   for(d[0]=1; d[0]<=9; d[0]++)
    {
      mpz_set_ui(e[0], d[0]);  
      mpz_mul_ui(h[0], D[M-ODD], d[0]); 

      int f = mpz_fdiv_ui(e[0], 5); 
                                    
      mpz_add(tmp, h[0], D[M-ODD]); 

      init_m1(h[0]); 
      init_m2(tmp);

      if (f==get_digit1(h[0], 0) || f==get_digit2(tmp, 0)) recur(1);
    }

   printf(" total time = %d sec.\t\t\t\n", clock()/1000); 
   getchar();
 }

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Patrick De Geest - Belgium

- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com