HOME plateWON | World!OfNumbers Factorization of thePalindromic Pentagonals Palindromic Pentagonals

Legend
```
F_ba  Decomposition of the basenumber in its prime factors.
F_pp  Decomposition of the palindromic pentagonal.
Note : a palindromic pentagonal will always be divisible by its basenumber when this
last one is 'odd'. With 'even' basenumbers you'll notice that the pentagonals
are always divisible by half their basenumbers.
To reconstruct the pentagonals you must take into account the green together with
the purple prime factors but not the black 2.
Date  Date of discovery by the author.
Hypertext links to related topics in number theory

```

Factorization
```
[76]
F_ba  829412616490882316063874786 =
2 * 3 * 17 * 8131496240106689373175243
F_pp  1031887932591377142105479799979745012417731952397881301 =
89 * 1619 * 7669 * 47497 * 47407834628939
Date  June 16, 2023 ( Patrick De Geest / CUDA code by Robert Xiao )

[75]
F_ba  219838383896945839241529093 =
3 * 11 * 19 * 350619432052545198152359
F_pp  72493372551631403519074864446847091530413615527339427 =
37 * 43 * 269 * 15643 * 49255221548658287
Date  January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[74]
F_ba  211567096617431127327768331 =
19 * 61 * 83 * 635057 * 3463170635320639
F_pp  67140954556694156338058353235385083365149665545904176 =
2 * 2 * 2 * 2 * 19834415307884168186978281
Date  January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[73]
F_ba  196744195862034221724924905 =
5 * 15443 * 506180999 * 5033782130833
F_pp  58062417908097725661820084648002816652779080971426085 =
55158679 * 301638047 * 17737532789
Date  January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[72]
F_ba  140815521353961270534020208 =
2 * 2 * 2 * 2 * 3 * 197 * 619 * 1442743 * 16674907714429
F_pp  29743516581281883860142882928824106838818218561534792 =
11 * 13 * 17566807 * 168167827918672423
Date  January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[71]
F_ba  123470453704578756803923204 =
2 * 2 * 23 * 2237 * 599941953045512996851
F_pp  22867429407021789074918527272581947098712070492476822 =
587 * 631024465270419540735553
Date  January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[70]
F_ba  115716935699622852551776543 =
37 * 1867 * 1675139126212348941817
F_pp  20085613811565974693953734743735939647956511831658002 =
2 * 13 * 107 * 12941 * 26183 * 2137049 * 86164691
Date  January 9, 2023 ( David Griffeath / CUDA code by Robert Xiao )

[69]
F_ba  1997352210935459325350510 =
2 * 5 * 59 * 80021 * 42305678889280109
F_pp  5984123781793151403874475744783041513971873214895 =
5992056632806377976051529
Date  December 6, 2022 ( Robert Xiao )

[68]
F_ba  1366335687983609354348844 =
2 * 2 * 3 * 3 * 13 * 53 * 4464754993 * 12337809427
F_pp  2800309818386464643692792972963464646838189030082 =
101 * 601 * 49991 * 1350799828027241
Date  December 6, 2022 ( Robert Xiao )

[67]
F_ba  1214693643268411793685388 =
2 * 2 * 71 * 73 * 3037 * 533327 * 36173222191
F_pp  2213220970495031472095671765902741305940790223122 =
337 * 42209 * 256184617678977811
Date  December 6, 2022 ( Robert Xiao )

[66]
F_ba  646108029840746975319151 =
19 * 31 * 1096957605841675679659
F_pp  626183379337037375893787787398573730733973381626 =
2 * 7 * 11 * 13 * 484096925455105126363
Date  November 11, 2022 ( David Griffeath / Rust code by Robert Xiao )

[65]
F_ba  386808141157899128841063 =
3 * 11 * 17 * 313 * 2749 * 18829687 * 42556957
F_pp  224430807099043827014991199410728340990708034422 =
2 * 199 * 36739 * 140143 * 283142493239
Date  November 11, 2022 ( David Griffeath / Rust code by Robert Xiao )

[64]
F_ba  128481111918761748263908 =
2 * 2 * 7 * 19 * 241505849471356669669
F_pp  24761094179822073249932323994237022897149016742 =
71 * 60659 * 11347379 * 7886991733
Date  January 6, 2008 ( Feng Yuan )

[63]
F_ba  4181240246129576678503 =
7 * 13 * 2053 * 22380757434200161
F_pp  26224154993780584443322334448508739945142262 =
2 * 11 * 91297 * 3122606024689831
Date  January 5, 2008 ( Feng Yuan )

[62]
F_ba  3166575018238865276806 =
2 * 7 * 1052893 * 1090217 * 197044609
F_pp  15040796019201704940688604940710291069704051 =
11 * 13 * 66431643739276893919
Date  November 11, 2022 ( Robert Xiao )

[61]
F_ba  1161338314703013743743 =
19 * 173 * 928159 * 380659497671
F_pp  2023060021795854282372732824585971200603202 =
2 * 9733 * 13901 * 6437648365279
Date  January 6, 2008 ( Feng Yuan )

[60]
F_ba  226255113072008674109 =
20929 * 22541 * 479597317681
F_pp  76787064286841145600200654114868246078767 =
339382669608013011163
Date  November 11, 2022 ( Robert Xiao )

[59]
F_ba  101908013398232552381 =
13 * 43 * 113 * 47431 * 34013850853
F_pp  15577864792161518113031181516129746877551 =
2843 * 53767857930829697
Date  January 3, 2008 ( Feng Yuan )

[58]
F_ba  32178927183122554461 =
3 * 3 * 3 * 3 * 3 * 11 * 12038506241347757
F_pp  1553225031985055486446845505891305223551 =
89 * 479 * 170341 * 6646884121
Date  January 3, 2008 ( Feng Yuan )

[57]
F_ba  12470286104989637219 =
61 * 17203 * 11883445896293
F_pp  233262053310446425999524644013350262332 =
2 * 2 * 13 * 13 * 719 * 1187 * 32422117201
Date  November 4, 2022 ( Robert Xiao )

[56]
F_ba  3225069471604675446 =
2 * 3 * 3 * 19 * 11311 * 833704154783
F_pp  15601609645014690722709641054690610651 =
11 * 463 * 24733 * 76808601073
Date  November 4, 2022 ( Robert Xiao )

[55]
F_ba  2215732656045463378 =
2 * 569 * 2221 * 876650607061
F_pp  7364206804599425576755249954086024637 =
7 * 83 * 11440960358238193
Date  November 4, 2022 ( Robert Xiao )

[54]
F_ba  642912991153879996 =
2 * 2 * 11 * 41 * 2042077 * 174519337
F_pp  620005671291643466664346192176500026 =
53 * 36391301386068679
Date  January 6, 2008 ( Feng Yuan )

[53]
F_ba  222497695855916654 =
2 * 11551 * 9631101023977
F_pp  74257836991787986368978719963875247 =
7 * 95356155366821423
Date  January 6, 2008 ( Feng Yuan )

[52]
F_ba  64541848291142556 =
2 * 2 * 3 * 37 * 3156121 * 46057969
F_pp  6248475271255291881925521725748426 =
7 * 11 * 11 * 13 * 17584737523697
Date  January 6, 2008 ( Feng Yuan )

[51]
F_ba  1343985615421963 =
179 * 563 * 13336233619
F_pp  2709446001691728271961006449072 =
2 * 2 * 2 * 2 * 510331 * 246895939
Date  April 2, 2002 ( Feng Yuan )

[50]
F_ba  1331901641608903 =
17 * 718007 * 109117537
F_pp  2660942974380735370834792490662 =
2 * 97 * 345133 * 29838377
Date  April 2, 2002 ( Feng Yuan )

[49]
F_ba  192460705375190 =
2 * 5 * 7 * 87797 * 31315861
F_pp  55561684670273437207648616555 =
29 * 41 * 1439 * 337458739
Date  August 5, 2000 ( Patrick De Geest )

[48]
F_ba  189271045290605 =
5 * 7573 * 4998575077
F_pp  53735292878097279087829253735 =
7 * 17 * 127447 * 18719699

[47]
F_ba  62640018209362 =
2 * 11 * 2847273554971
F_pp  5885657821903773091287565885 =
5 * 13 * 13 * 97 * 2292686569

[46]
F_ba  62407875352937 =
3041 * 20522155657
F_pp  5842114359101551019534112485 =
5 * 11 * 1702032964171

[45]
F_ba  22073207482889 =
64609 * 341642921
F_pp  730839732873989378237938037 =
33109811224333

[44]
F_ba  8505462902906 =
2 * 4252731451453
F_pp  108514348789060987843415801 =
1229 * 20761911073

[43]
F_ba  6106091136277 =
11 * 293 * 1894536499
F_pp  55926523446777764432562955 =
5 * 199 * 9205162517

[42]
F_ba  3690877000943 =
11 * 101 * 3322121513
F_pp  20433859554133145595833402 =
2 * 1327 * 2293 * 909737

[41]
F_ba  2704211220546 =
2 * 3 * 3 * 11 * 6907 * 1977361
F_pp  10969137487988978473196901 =
8112633661637

[40]
F_ba  2269269065474 =
2 * 47 * 349 * 69172379
F_pp  7724373137274727313734277 =
7 * 11 * 233 * 239 * 1587679

[39]
F_ba  2118668671851 =
3 * 107 * 31817 * 207443
F_pp  6733135411623261145313376 =
2 * 2 * 2 * 2 * 2 * 66271 * 1498583

[38]
F_ba  1199186171664 =
2 * 2 * 2 * 2 * 3 * 13 * 37 * 463 * 112181
F_pp  2157071211464641121707512 =
7 * 53 * 9696923221

[37]
F_ba  100208264581 =
2383 * 42051307
F_pp  15062544435453444526051 =
7 * 13 * 29 * 56958089

[36]
F_ba  72507025789 =
11 * 9871 * 667769
F_pp  7885903183113813095887 =
71 * 613 * 2498921

[35]
F_ba  20483169156 =
2 * 2 * 3 * 3 * 23 * 2851 * 8677
F_pp  629340327999723043926 =
401 * 153240667

[34]
F_ba  18517422797 =
23 * 805105339
F_pp  514342420555024243415 =
5 * 42641 * 130279

[33]
F_ba  18306458265 =
3 * 5 * 107 * 157 * 72649
F_pp  502689621303126986205 =
127 * 216218011

[32]
F_ba  6693818696 =
2 * 2 * 2 * 367 * 2279911
F_pp  67210813099031801276 =
7 * 11 * 11 * 29 * 817549

[31]
F_ba  2049123156 =
2 * 2 * 3 * 127 * 1344569
F_pp  6298358561658538926 =
6147369467

[30]
F_ba  1345679688 =
2 * 2 * 2 * 3 * 56069987
F_pp  2716280733370826172 =
311 * 317 * 40949

[29]
F_ba  851649306 =
2 * 3 * 17 * 47 * 59 * 3011
F_pp  1087959810189597801 =
19 * 67 * 2007029

[28]
F_ba  818049201 =
3 * 6449 * 42283
F_pp  1003806742476083001 =
1227073801

[27]
F_ba  700457153 =
11 * 457 * 139339
F_pp  735960334433069537 =
101 * 10402829

[26]
F_ba  316882086 =
2 * 3 * 23 * 2296247
F_pp  150621384483126051 =
11 * 86422387

[25]
F_ba  225563533 =
13 * 31 * 347 * 1613
F_pp  76318361016381367 =
577 * 586387

[24]
F_ba  100058581 =
7 * 257 * 55619
F_pp  15017579397571051 =
839 * 178889

[23]
F_ba  84885761 =
827 * 102643
F_pp  10808388588380801 =
11 * 2647 * 4373

[22]
F_ba  59401650 =
2 * 3 * 5 * 5 * 7 * 11 * 37 * 139
F_pp  5292834004382925 =
13 * 1619 * 8467

[21]
F_ba  13280839 =
11 * 11 * 13 * 8443
F_pp  264571020175462 =
2 * 7 * 61 * 23327

[20]
F_ba  2684561 =
11 * 109 * 2239
F_pp  10810300301801 =
7 * 13 * 17 * 19 * 137

[19]
F_ba  1979130 =
2 * 3 * 5 * 37 * 1783
F_pp  5875432345785 =
5937389

[18]
F_ba  1965117 =
3 * 7 * 11 * 47 * 181
F_pp  5792526252975 =
5 * 5 * 157 * 751

[17]
F_ba  1258723 =
PRIME
F_pp  2376574756732 =
2 * 2 * 11 * 11 * 47 * 83

[16]
F_ba  44059 =
PRIME
F_pp  2911771192 =
2 * 2 * 2 * 11 * 751

[15]
F_ba  31926 =
2 * 3 * 17 * 313
F_pp  1528888251 =
11 * 8707

[14]
F_ba  26906 =
2 * 11 * 1223
F_pp  1085885801 =
7 * 13 * 887

[13]
F_ba  26466 =
2 * 3 * 11 * 401
F_pp  1050660501 =
79397

[12]
F_ba  6010 =
2 * 5 * 601
F_pp  54177145 =
11 * 11 * 149

[11]
F_ba  4228 =
2 * 2 * 7 * 151
F_pp  26811862 =
11 * 1153

[10]
F_ba  2229 =
3 * 743
F_pp  7451547 =
3343

[9]
F_ba  2173 =
41 * 53
F_pp  7081807 =
3259

[8]
F_ba  693 =
3 * 3 * 7 * 11
F_pp  720027 =
1039

[7]
F_ba  101 =
PRIME
F_pp  15251 =
151

[6]
F_ba  44 =
2 * 2 * 11
F_pp  2882 =
131

[5]
F_ba  26 =
2 * 13
F_pp  1001 =
7 * 11

[4]
F_ba  4 =
2 * 2
F_pp  22 =
11

[3]
F_ba  2 =
PRIME
F_pp  5 =
PRIME

[2]
F_ba  1 =
1
F_pp  1 =
1

[1]
F_ba  0 =
0
F_pp  0 =
0

```