All the prime factors of the Smarandache Concatenated Numbers upto the first not factored

World!Of Numbers		HOME plate WON \|
Normal Smarandache Concatenated Numbers Prime factors from 1 upto n (n=2,3,...,98)
Reversed Smarandache Concatenated Numbers Repunits Factorization

sm1	sm2	sm3	sm4	sm5	sm6	sm7	sm8	sm9	sm10	sm11	sm12	sm13	sm14	sm15	sm16	sm17	sm18	sm19	sm20
sm21	sm22	sm23	sm24	sm25	sm26	sm27	sm28	sm29	sm30	sm31	sm32	sm33	sm34	sm35	sm36	sm37	sm38	sm39	sm40
sm41	sm42	sm43	sm44	sm45	sm46	sm47	sm48	sm49	sm50	sm51	sm52	sm53	sm54	sm55	sm56	sm57	sm58	sm59	sm60
sm61	sm62	sm63	sm64	sm65	sm66	sm67	sm68	sm69	sm70	sm71	sm72	sm73	sm74	sm75	sm76	sm77	sm78	sm79	sm80
sm81	sm82	sm83	sm84	sm85	sm86	sm87	sm88	sm89	sm90	sm91	sm92	sm93	sm94	sm95	sm96	sm97	sm98	sm99	sm100
sm101	sm102	sm103	sm104	sm105	sm106	sm107	sm108	sm109	sm110	sm111	sm112	sm113	sm114	sm115	sm116	sm117	sm118	sm119	sm120
sm121	sm122	sm123	sm124	sm125	sm126	sm127	sm128	sm129	sm130	sm131	sm132	sm133	sm134	sm135	sm136	sm137	sm138	sm139	sm140
sm141	sm142	sm143	sm144	sm145	sm146	sm147	sm148	sm149	sm150	sm151	sm152	sm153	sm154	sm155	sm156	sm157	sm158	sm159	sm160
sm161	sm162	sm163	sm164	sm165	sm166	sm167	sm168	sm169	sm170	sm171	sm172	sm173	sm174	sm175	sm176	sm177	sm178	sm179	sm180
sm181	sm182	sm183	sm184	sm185	sm186	sm187	sm188	sm189	sm190	sm191	sm192	sm193	sm194	sm195	sm196	sm197	sm198	sm199	sm200

Legend

sm_N if N less than 99 - complete factorization is given on this page

sm_N if N is above 99 - refer for the complete factorization to M. Fleuren page

sm_N smallest Sm with unknown factors

sm_N Sm with unknown factors (ref. M. Fleuren's page)

sm_N Sm with new complete factorization : see list at end of page

sm_N Sm with a new factor but still incomplete : consult Messages section

sm_N	if N less than 99 - complete factorization is given on this page
sm_N	if N is above 99 - refer for the complete factorization to M. Fleuren page
sm_N	smallest Sm with unknown factors
sm_N	Sm with unknown factors (ref. M. Fleuren's page)
sm_N	Sm with new complete factorization : see list at end of page
sm_N	Sm with a new factor but still incomplete : consult Messages section

Prefatory notes

In the table below you'll find all the prime factors of the concatenation
of numbers from 1 upto n.
These numbers are called Smarandache Concatenated Numbers.

The first one with an unknown prime factor is when n = 99.
If there is a breaktrough in partially or completely factorising Sm99, please let me know,
so that I can update the list.

For the factorizations I also followed the sources from

Micha Fleuren, Smarandache factors

Hans Havermann, Factorization of Smarandache Concatenated Numbers, Sm-n (n < 84)

Other subject related sources on the web :

Smarandache Numbers by Dr. M. L. Perez
Smarandache factors by Micha Fleuren
Primes by Listing by Carlos Rivera
Consecutive Number Sequences by Eric W. Weisstein
Smarandache Sequences by Eric W. Weisstein
List of factors of the Reversed Smarandache Concatenated Numbers by Patrick De Geest

Book sources :

"Some Notions and Questions in Number Theory", by C.Dumitrescu and V.Seleacu, Glendale, AZ:Erhus University Press, 1994. (communicated to me by Marin Petrescu from Bucharest)

"CRC Concise Encyclopedia of Mathematics", by Eric W. Weisstein, CRC Press, Boca Raton, Florida, 1998. (communicated to me by M.L. Perez)

Factorization websites

NFSNET - Number Field Sieve
GGNFS - A Number Field Sieve implementation
GMP-ECM 6.0.1

Messages

[ December 9, 2007 ]
Greg Childers (email) factorized Sm94 ! [ goto entry ]

Hi Patrick,

Here are the factors of Sm94. This was completed using SNFS.
GGNFS was used for the sieving and msieve for the post-processing.

p79: 1825097233762709447432521941926649289213154260264910537140594516431173070300371

p82: 2674525573684858697560701870658348933916102325593721165422426453989766526938215889

Greg

[ June 8, 2006 ]
Sean A. Irvine (email)

Excellent work! (reg. Sm98 by Ph. Strohl)

Sm94 is still struggling. My yield has dropped below 1 and I've sieved
to special-q 70M already, but still don't have enough relations.

S.

[ June 6, 2006 ]
Philippe Strohl (email)

Hi Patrick !
I have factorized the remaining part of the 98th Smarandache
concatenated number. It was a 126 digits composite.
I have broken it with ggnfs (a wonderful program : I have done it with
a common laptop computer with "only" 512 megs of ram and a 1.4 GHz
celeron M in two weeks).

the results :
N = 709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707
( 126 digits)
Divisors found:
r1=3588472635471667861938967869443938442910813342994227048889 (pp58)
r2=197825482406769698151783117995020967519766027202915861687264259155363 (pp69)
Version: GGNFS-0.77.1-20060513-pentium-m
(prp verified prime with apr-cl)

Thanks for your site and for keeping tracks of our work.
Best regards.

Philippe Strohl

[ September 11, 2005 ]
Sean A. Irvine (email)

The next two have finished:

Sm87 C145 =
(p51) * (p95)
by SNFS, 14 days
Sm88 C153 =
(p42) * (p51) * (p61)
by GNFS, 8 hours

Sm90 looks like it will have to be SNFS since ECM has failed
to find a factor.

Regards,
Sean.

[ August 29, 2005 ]
Philippe Strohl (email)

Hi Patrick !
Thanks for accepting my "colouring" idea ! I am very pleased !

I should report you this 39 digits factor for Sm98 (Partial factorization):

Sm98* 2.3^2.23.37.199
p16: 1495444452918817(MF)
c165: 270825497607069872452415496119443135107702791840293286471110488510
4768274391266695197120574357173627794391936143016235446328574795690351940341420
23605896434694145167
Line=16/32 Curves=47/1000 B1=1000000 factors=0
C165 Using B1=1000000, B2=839549780, polynomial Dickson(6), sigma=594918519
Step 1 took 28422ms
Step 2 took 18926ms
********** Factor found in step 2: 381502754125464943168932369122248696781
Found probable prime factor of 39 digits:
381502754125464943168932369122248696781

Composite cofactor
709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707
has 126 digits

Thanks again.
Best regards.
Philippe Strohl

[ August 29, 2005 ]
Sean A. Irvine (email)

Here is the last part of Sm86:

10828687641092318839822035841363590407263202742239027773 (p56) *
1089075252400674157091531724111232381528208779232955680665273 (p61)
by GNFS, 2 days.

As before I'm now working on Sm87.

Sean.

[ August 28, 2005 ]
Sean A. Irvine (email) latest results.

Here are my latest results. Like I mentioned earlier
I expect to complete Sm86 today as well:

Sm83 C134
21875480270521598141087357354188092945840550359281483 (p53) *
3966169790267211790412249283896602109358687165012835285295541472324348526743126307 (p82)
by SNFS, 8 days

Sm85 C158 =
120549814855596987772827562271063563633851059 (p45) *
Using B1=11000000, sigma=1708124291
2112809210944968177871685727287164545437750155430310661 (p55) *
197843626412162026434764405036310959588059884460495810550047 (p60)
by GNFS, 1 day

Sm86 C154 =
718252229986396496762902999331863301257 (p39) * C116
Using B1=11000000, sigma=3414478964
C116 by GNFS nearly done

Sm87 C145 Sieving by SNFS started 2005-08-29.

Others with B1=1e6 (I have now completed 1000 curves with B1=1e6
on all Sm(n), n <= 200)

Sm114 8678622406220213516465050301044327
Sm159 45941358846148651407783221723920871719
Sm171 40202471819457246557501649563881337
Sm193 5167315927941164272437909427556797

Sean.

It seems that a fierce competition is going on. But to avoid
duplicate work and loose valuable cpu time I advice strongly
to make arrangements among yourselves!

[ August 28, 2005 ]
Philippe Strohl (email)

..., for example : the smallest unfactored Sm number is sm83
(unfactored) but I have factored last year Sm85 (involving a p45 found by
ecm) and Sm86 (with a p39 and a ggnfs on the remaining c115)... This
represents quite a large amount of cpu work. Sm84 factorization is still
known on M Fleuren page...

[ August 3, 2005 ]
Sean A. Irvine (email) completely factorized Sm78 ! [ goto entry ]

Sm78 C139 =
205155431830422787082756234197593935249202704547671264423 (p57) *
17403902113720391120287411398887911225298966708915583006414519403038472992542973083 (p83)
by GNFS (General Number Field Sieve), 9 days

Here is a bunch more factors for higher values which I have not seen
previously reported. All these were found with ECM B1=1e6.

Sm89 496118159817126721484175235476073
Sm89 26459905787227421825352754831024262009257.P64
Sm92 46731404628893905607210235741707
Sm93 19544056951015647623992763251
Sm95 244987542265129586458446183157595351.P141
Sm100 970447246795177523033247400823.P118
Sm106 95383501607400293616004374931
Sm106 54259599094002572583355411045946413
Sm108 132761751746390611923240080737166083.P161
Sm109 9943216978062352390003139833531
Sm114 2042059881000388200555074336219
Sm116 9787002048140152171263515060558503699.P198
Sm121 105299178204417486675841093021769.P214
Sm123 12347002211187670552593982429
Sm123 2829927788416784955921382453753
Sm125 295999706346724665505289
Sm137 144065103514544138702103468451
Sm148 8817212782626223819399721069204897.P254
Sm152 4103096315830350734534473515557
Sm152 12805089500421274253268517941967
Sm152 17815076027044127272632744936161.P205
Sm154 32063206397901252963254536935569
Sm159 11855111297257593607972759339201
Sm160 64603936118676024484144135734907
Sm162 22260247937572504750086047
Sm164 1039418554780603268384723777072953
Sm165 13183356310254866666237435750357.P328
Sm176 1011379313630785579015894871
Sm183 553245689211853052761209813199
Sm184 677008100402429325901609057.P342
Sm187 1080829169904060835770214147747.P411
Sm193 419908232491384495189
Sm195 165897663095213559529993681.P412
Sm198 14158849264684185910199571953

Further, after studying Backstrom's work on Rsm76 I am now able to generate
SNFS polynomials for all the remaining Sm numbers below 100. It would have
been much faster to do Sm78 by SNFS, but I had already started it before
working out how to apply SNFS to the number. It should be possible to complete
all values up to Sm(100) by SNFS, although a few will be quite difficult runs.

The next smallest unfactored number of this form is now Sm83 [ C134 ].

Sean.

[ November 18, 2004 ]
Sean A. Irvine (email) completely factorized Sm75 ! [ goto entry ]

It took him 13 days, by using GNFS.
Well done, congratulations for factoring Sm75(c133) into this p47 * p87 :
38824496309870038690197243565592769246963314017 (p47) *
219358378032318168161320006998916878634145966511629131235131312083699783021949850982403 (p87)

Next challenge is this composite factor of 139 digits of Sm78 :
3570505053674714753162296261527331568459971771942/
9181309659088118527251315326728064046015264067596/
03889145976969679985423963150530264526109

[ March 23, 2004 ]
Philippe Strohl (email) completely factorized Sm73 ! [ goto entry ]

Hello Patrick !

This mail to inform you that the factorization of the 73th concatenated smarandache number is now complete
with the discovery of a p46 by GMP-ECM...

Sm73 = 37907.p46.p87
p46: 1612352371081094864112011094480307952600705089
p87: 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851
...
Sm74 factorization is known and the next composite to challenge is Sm75
with no factors expected below 35 digits...

Sm74 = 2.3.7.1788313.21565573.p20.p25.p31.p49
p20: 99014155049267797799
p25: 1634187291640507800518363(PZ)
p31: 1981231397449722872290863561307
p49: 2377534541508613492655260491688014802698908815817

Sm75* 3.5^2.193283.c133
c133:
851647853845481367839983983361331811035304896846801931077529055832/
3936344974946612980172082837107906069172212808249295700548030242851

The list of Sm factors


 1
1

Sm1 = p1 = unity

1

 12
2²
3

Sm2 = (p1)^2 * p1
2^2 * 

3

 123
3
41

Sm3 = p1 * p2 = semiprime
3 * 

41

 1234
2
617

Sm4 = p1 * p3 = semiprime
2 * 

617

 12345
3
5
823

Sm5 = p1 * p1 * p3
3 * 
5 * 

823

 123456
2⁶
3
643

Sm6 = (p1)^6 * p1 * p3
2^6 * 
3 * 

643

 1234567
127
9.721

Sm7 = p3 * p4 = semiprime
127 * 

9721

 12345678
2
3²
47
14.593

Sm8 = p1 * (p1)^2 * p2 * p5
2 * 
3^2 * 
47 * 

14593

 123456789
3²
3.607
3.803

Sm9 = (p1)^2 * p4 * p4
3^2 * 
3607 * 

3803

 12345678910
2
5
1.234.567.891

Sm10 = p1 * p1 * p10
2 * 
5 * 

1234567891

 1234567891011
3
7
13
67
107
630.803

Sm11 = p1 * p1 * p2 * p2 * p3 * p6
3 * 
7 * 
13 * 
67 * 
107 * 

630803

 1234567...12
2³
3
2.437
2.110.805.449

Sm12 = (p1)^3 * p1 * p4 * p10
2^3 * 
3 * 
2437 * 

2110805449

 1234567...13
113
125.693
869.211.457

Sm13 = p3 * p6 * p9
113 * 
125693 * 

869211457

 1234567...14
2
3
205.761.315.168.520.219

Sm14 = p1 * p1 * p18
2 * 
3 * 

205761315168520219

 1234567...15
3
5
8.230.452.606.740.808.761

Sm15 = p1 * p1 * p19
3 * 
5 * 

8230452606740808761

 1234567...16
2²
2.507.191.691
1.231.026.625.769

Sm16 = (p1)^2 * p10 * p13
2^2 * 

2507191691 * 

1231026625769

 1234567...17
3²
47
4.993
584.538.396.786.764.503

Sm17 = (p1)^2 * p2 * p4 * p18
3^2 * 
47 * 
4993 * 

584538396786764503

 1234567...18
2
3²
97
88.241
801.309.546.900.123.763

Sm18 = p1 * (p1)^2 * p2 * p5 * p18
2 * 
3^2 * 
97 * 
88241 * 

801309546900123763

 1234567...19
13
43
79
281
1.193
833.929.457.045.867.563

Sm19 = p2 * p2 * p2 * p3 * p4 * p18
13 * 
43 * 
79 * 
281 * 
1193 * 

833929457045867563

 1234567...20
2⁵
3
5
323.339
3.347.983
2.375.923.237.887.317

Sm20 = (p1)^5 * p1 * p1 * p6 * p7 * p16
2^5 * 
3 * 
5 * 
323339 * 
3347983 * 

2375923237887317

 1234567...21
3
17
37
43
103
131
140.453
802.851.238.177.109.689

Sm21 = p1 * p2 * p2 * p2 * p3 * p3 * p6 * p18
3 * 
17 * 
37 * 
43 * 
103 * 
131 * 
140453 * 

802851238177109689

 1234567...22
2
7
1.427
3.169
85.829
2.271.991.367.799.686.681.549

Sm22 = p1 * p1 * p4 * p4 * p5 * p22
2 * 
7 * 
1427 * 
3169 * 
85829 * 

2271991367799686681549

 1234567...23
3
41
769
13.052.194.181.136.110.820.214.375.991.629

Sm23 = p1 * p2 * p3 * p32
3 * 
41 * 
769 * 

13052194181136110820214375991629

 1234567...24
2²
3
7
978.770.977.394.515.241
1.501.601.205.715.706.321

Sm24 = (p1)^2 * p1 * p1 * p18 * p19
2^2 * 
3 * 
7 * 

978770977394515241 * 

1501601205715706321

 1234567...25
5²
15.461
31.309.647.077
1.020.138.683.879.280.489.689.401

Sm25 = (p1)^2 * p5 * p11 * p25
5^2 * 
15461 * 

31309647077 * 

1020138683879280489689401

 1234567...26
2
3⁴
21.347
2.345.807
982.658.598.563
154.870.313.069.150.249

Sm26 = p1 * (p1)^4 * p5 * p7 * p12 * p18
2 * 
3^4 * 
21347 * 
2345807 * 

982658598563 * 

154870313069150249

 1234567...27
3³
19²
4.547
68.891
40.434.918.154.163.992.944.412.000.742.833

Sm27 = (p1)^3 * (p2)^2 * p4 * p5 * p32
3^3 * 
19^2 * 
4547 * 

68891 * 

40434918154163992944412000742833

 1234567...28
2³
47
409
416.603.295.903.037
192.699.737.522.238.137.890.605.091

Sm28 = (p1)^3 * p2 * p3 * p15 * p27
2^3 * 
47 * 
409 * 

416603295903037 * 

192699737522238137890605091

 1234567...29
3
859
24.526.282.862.310.130.729
19.532.994.432.886.141.889.218.213

Sm29 = p1 * p3 * p20 * p26
3 * 
859 * 

24526282862310130729 * 

19532994432886141889218213

 1234567...30
2
3
5
13
49.269.439
370.677.592.383.442.753
17.333.107.067.824.345.178.861

Sm30 = p1 * p1 * p1 * p2 * p8 * p18 * p23
2 * 
3 * 
5 * 
13 * 

49269439 * 

370677592383442753 * 

17333107067824345178861

 1234567...31
29
2.597.152.967
163.915.283.880.121.143.989.433.769.727.058.554.332.
    117

Sm31 = p2 * p10 * p42
29 * 
2597152967 * 

163915283880121143989433769727058554332117

 1234567...32
2²
3
7
45.068.391.478.912.519.182.079
326.109.637.274.901.966.196.516.045.637

Sm32 = (p1)^2 * p1 * p1 * p23 * p30
2^2 * 
3 * 
7 * 

45068391478912519182079 * 

326109637274901966196516045637

 1234567...33
3
23
269
7.547
116.620.853.190.351.161
7.557.237.004.029.029.700.530.634.132.859

Sm33 = p1 * p2 * p3 * p4 * p18 * p31
3 * 
23 * 
269 * 
7547 * 

116620853190351161 * 

7557237004029029700530634132859

 1234567...34
2
6.172.839.455.055.606.570.758.085.909.601.061.116.
  212.631.364.146.515.661.667

Sm34 = p1 * p58 = semiprime
2 * 

6172839455055606570758085909601061116212631364146515661667

 1234567...35
3²
5
139
151
64.279.903
4.462.548.227
4.556.722.495.899.317.991.381.926.119.681.186.927

Sm35 = (p1)^2 * p1 * p3 * p3 * p8 * p10 * p37
3^2 * 
5 * 
139 * 
151 * 
64279903 * 
4462548227 * 

4556722495899317991381926119681186927

 1234567...36
2⁴
3²
103
211
39.448.709.943.503.776.711.542.648.338.171.477.043.
   440.283.875.433.388.943

Sm36 = (p1)^4 * (p1)^2 * p3 * p3 * p56
2^4 * 
3^2 * 
103 * 
211 * 

39448709943503776711542648338171477043440283875433388943

 1234567...37
71
12.379
4.616.929
3.042.410.911.077.206.144.807.069.396.988.766.146.
  557.218.727.107.817

Sm37 = p2 * p5 * p7 * p52
71 * 
12379 * 

4616929 * 

3042410911077206144807069396988766146557218727107817

 1234567...38
2
3
86.893.956.354.189.878.775.643
2.367.958.875.411.463.048.104.007.458.352.976.869.124.
  861

Sm38 = p1 * p1 * p23 * p43
2 * 
3 * 

86893956354189878775643 * 

2367958875411463048104007458352976869124861

 1234567...39
3
67
311
1.039
6.216.157.781.332.031.799.688.469
305.788.363.093.026.251.381.516.836.994.235.539

Sm39 = p1 * p2 * p3 * p4 * p25 * p36
3 * 
67 * 
311 * 
1039 * 

6216157781332031799688469 * 

305788363093026251381516836994235539

 1234567...40
2²
5
3.169
60.757
579.779
4.362.289.433
79.501.124.416.220.680.469
15.944.694.111.943.672.435.829.023

Sm40 = (p1)^2 * p1 * p4 * p5 * p6 * p10 * p20 * p26
2^2 * 
5 * 
3169 * 
60757 * 
579779 * 
4362289433 * 

79501124416220680469 * 

15944694111943672435829023

 1234567...41
3
487
493.127
32.002.651
53.545.135.784.961.981.058.419.604.998.638.516.483.
   529.257.158.438.201.753

Sm41 = p1 * p3 * p6 * p8 * p56
3 * 
487 * 
493127 * 
32002651 * 

53545135784961981058419604998638516483529257158438201753

 1234567...42
2
3
127
421
22.555.732.187
4.562.371.492.227.327.125.110.177
3.739.644.646.350.764.691.998.599.898.592.229

Sm42 = p1 * p1 * p3 * p3 * p11 * p25 * p34
2 * 
3 * 
127 * 
421 * 
22555732187 * 

4562371492227327125110177 * 

3739644646350764691998599898592229

 1234567...43
7
17
449
231.058.353.953.907.153.927.797.941.629.430.896.528.
    705.484.237.484.443.924.582.239.474.910.453

Sm43 = p1 * p2 * p3 * p72
7 * 
17 * 
449 * 

231058353953907153927797941629430896528705484237484443924582239474910453

 1234567...44
2³
3²
12.797.571.009.458.074.720.816.277
1.339.846.151.380.678.925.030.581.935.625.950.075.
  102.697.197.563.351

Sm44 = (p1)^3 * (p1)^2 * p26 * p52
2^3 * 
3^2 * 

12797571009458074720816277 * 

1339846151380678925030581935625950075102697197563351

 1234567...45
3²
5
7
41
727
1.291
2.634.831.682.519
379.655.178.169.650.473
10.181.639.342.830.457.495.311.038.751.840.866.580.
   037

Sm45 = (p1)^2 * p1 * p1 * p2 * p3 * p4 * p13 * p18 * p41
3^2 * 
5 * 
7 * 
41 * 
727 * 
1291 * 

2634831682519 * 

379655178169650473 * 

10181639342830457495311038751840866580037

 1234567...46
2
31
103
270.408.101
374.332.796.208.406.291
3.890.951.821.355.123.413.169.209
4.908.543.378.923.330.485.082.351.119

Sm46 = p1 * p2 * p3 * p9 * p18 * p25 * p28
2 * 
31 * 
103 * 

270408101 * 

374332796208406291 * 

3890951821355123413169209 * 

4908543378923330485082351119

 1234567...47
3
4.813
679.751
4.626.659.581.180.187.993.501
27.186.948.196.033.729.596.487.563.460.186.407.241.
   534.572.026.740.723

Sm47 = p1 * p4 * p6 * p22 * p53
3 * 
4813 * 

679751 * 

4626659581180187993501 * 

27186948196033729596487563460186407241534572026740723

 1234567...48
2²
3
179
1.493
1.894.439
15.771.940.624.188.426.710.323.588.657
1.288.413.105.003.100.659.990.273.192.963.354.903.
  752.853.409

Sm48 = (p1)^2 * p1 * p3 * p4 * p7 * p29 * p46
2^2 * 
3 * 
179 * 

1493 * 
1894439 * 

15771940624188426710323588657 * 

1288413105003100659990273192963354903752853409

 1234567...49
23
109
3.251.653
2.191.196.713
53.481.597.817.014.258.108.937
12.923.219.128.084.505.550.382.930.974.691.083.231.
   834.648.599

Sm49 = p2 * p3 * p7 * p10 * p23 * p47
23 * 
109 * 

3251653 * 

2191196713 * 

53481597817014258108937 * 

12923219128084505550382930974691083231834648599

 1234567...50
2
3
5²
13
211
20.479
160.189.818.494.829.241
46.218.039.785.302.111.919
19.789.860.528.346.995.527.543.912.534.464.764.790.
   909.391

Sm50 = p1 * p1 * (p1)^2 * p2 * p3 * p5 * p18 * p20 * p44
2 * 
3 * 
5^2 * 
13 * 
211 * 
20479 * 

160189818494829241 * 

46218039785302111919 * 

19789860528346995527543912534464764790909391

 1234567...51
3
17.708.093.685.609.923.339
2.323.923.950.500.978.408.934.946.776.574.079.545.
  611.397.611.995.364.705.071.565.292.612.305.003

Sm51 = p1 * p20 * p73
3 * 

17708093685609923339 * 

2323923950500978408934946776574079545611397611995364705071565292612305003

 1234567...52
2⁷
43.090.793.230.759.613
2.238.311.464.092.386.636.761.884.511.894.978.048.
  448.617.178.182.150.344.531.477.542.781.856.216.
  843

Sm52 = (p1)^7 * p17 * p76
2^7 * 

43090793230759613 * 

2238311464092386636761884511894978048448617178182150344531477542781856216843

 1234567...53
3³
7³
127.534.541.853.151.177
1.045.271.879.581.348.729.278.017.817.925.065.799.
  872.257.805.888.381.045.072.615.907.010.178.634.
  849

Sm53 = (p1)^3 * (p1)^3 * p18 * p76
3^3 * 
7^3 * 

127534541853151177 * 

1045271879581348729278017817925065799872257805888381045072615907010178634849

 1234567...54
2
3⁶
79
389
3.167
13.309
69.526.661.707
8.786.705.495.566.261.913.717
107.006.417.566.370.797.549.761.092.803.112.128.112.
    769.421.435.739

Sm54 = p1 * (p1)^6 * p2 * p3 * p4 * p5 * p11 * p22 * p51
2 * 
3^6 * 
79 * 
389 * 
3167 * 
13309 * 
69526661707 * 

8786705495566261913717 * 

107006417566370797549761092803112128112769421435739

 1234567...55
5
768.643.901
641.559.846.437.453
1.187.847.380.143.694.126.117
4.215.236.719.202.000.513.320.239.996.510.510.828.
  557.825.033.460.062.191

Sm55 = p1 * p9 * p15 * p22 * p55
5 * 
768643901 * 

641559846437453 * 

1187847380143694126117 * 

4215236719202000513320239996510510828557825033460062191

 1234567...56
2²
3
4.324.751.743.617.631.024.407.823
23.788.800.764.365.032.854.813.369.830.458.732.886.
   158.417.401.021.113.465.643.479.155.975.828.316.
   681

Sm56 = (p1)^2 * p1 * p25 * p77
2^2 * 
3 * 

4324751743617631024407823 * 

23788800764365032854813369830458732886158417401021113465643479155975828316681

 1234567...57
3
17
36.769.067
2.205.251.248.721
2.128.126.623.795.388.466.914.401.931.224.151.279
14.028.351.843.196.901.173.601.082.244.449.305.344.
   230.057.319

Sm57 = p1 * p2 * p8 * p13 * p37 * p47
3 * 
17 * 
36769067 * 

2205251248721 * 

2128126623795388466914401931224151279 * 

14028351843196901173601082244449305344230057319

 1234567...58
2
13
1.448.595.612.076.564.044.790.098.185.437
327.789.067.063.631.145.720.134.335.581.588.856.152.
    921.479.945.230.066.396.717.484.857.630.796.759

Sm58 = p1 * p2 * p31 * p75
2 * 
13 * 

1448595612076564044790098185437 * 

327789067063631145720134335581588856152921479945230066396717484857630796759

 1234567...59
3
340.038.104.073.949.513
324.621.819.487.091.567.830.636.828.971.096.713
3.728.107.520.554.143.574.058.126.525.447.653.708.
  074.390.492.098.041.537

Sm59 = p1 * p18 * p36 * p55
3 * 

340038104073949513 * 

324621819487091567830636828971096713 * 

3728107520554143574058126525447653708074390492098041537

 1234567...60
2³
3
5
97
157
67.555.753.880.267.981.819.314.968.257.940.564.232.
   852.139.165.917.171.861.439.543.181.780.049.107.
   204.700.168.947.673.874.146.559.500.327

Sm60 = (p1)^3 * p1 * p1 * p2 * p3 * p104
2^3 * 
3 * 
5 * 
97 * 
157 * 

67555753880267981819314968257940564232852139165917171861439543181780049107204700168947673874146559500327

 1234567...61
10.386.763
35.280.457.769.357
33.689.963.756.771.087.787.406.890.988.794.422.071.
   942.750.389.483.226.687.410.462.898.596.940.470.
   571.223.420.915.460.371

Sm61 = p8 * p14 * p92
10386763 * 

35280457769357 * 

33689963756771087787406890988794422071942750389483226687410462898596940470571223420915460371

 1234567...62
2
3²
1.709
329.167
1.830.733
9.703.956.232.921.821.226.401.223.348.541.281
6.862.941.251.271.421.600.892.952.202.464.376.235.
  224.342.144.596.167.046.191.804.311

Sm62 = p1 * (p1)^2 * p4 * p6 * p7 * p34 * p64
2 * 
3^2 * 
1709 * 
329167 * 
1830733 * 

9703956232921821226401223348541281 * 

6862941251271421600892952202464376235224342144596167046191804311

 1234567...63
3²
17.028.095.263
2.435.984.189.933.032.657.913.735.712.547.671.618.
  367.909
330.698.276.590.517.405.413.770.500.371.046.766.676.
    563.523.569.978.590.938.716.221

Sm63 = (p1)^2 * p11 * p43 * p63
3^2 * 
17028095263 * 

2435984189933032657913735712547671618367909 * 

330698276590517405413770500371046766676563523569978590938716221

 1234567...64
2²
7
17
19
197
522.673
1.072.389.445.090.071.307
20.203.723.083.803.464.811.983.788.589
611.891.180.337.745.942.599.768.541.236.768.900.814.
    521.123.060.392.220.304.537

Sm64 = (p1)^2 * p1 * p2 * p2 * p3 * p6 * p19 * p29 * p60
2^2 * 
7 * 
17 * 
19 * 
197 * 
522673 * 

1072389445090071307 * 

20203723083803464811983788589 * 

611891180337745942599768541236768900814521123060392220304537

 1234567...65
3
5
31
83.719
8.018.741.962.917.674.781.000.851.595.476.715.337.
  223.177
3.954.865.825.608.609.239.925.917.139.441.010.044.
  747.553.878.722.812.487.568.124.023.324.127

Sm65 = p1 * p1 * p2 * p5 * p43 * p70
3 * 
5 * 
31 * 
83719 * 

8018741962917674781000851595476715337223177 * 

3954865825608609239925917139441010044747553878722812487568124023324127

 1234567...66
2
3
7
20.143
971.077
319.873.117.219.722.504.963.051.951.872.747.251
927.600.480.728.565.729.398.211.282.118.577.179
506.464.674.142.683.362.314.480.915.373.647.544.917

Sm66 = p1 * p1 * p1 * p5 * p6 * p36 * p36 * p39
2 * 
3 * 
7 * 
20143 * 
971077 * 

319873117219722504963051951872747251 * 

927600480728565729398211282118577179 * 

506464674142683362314480915373647544917

 1234567...67
397
183.783.139.772.372.071
169.207.186.381.096.030.569.641.287.629.182.352.063.
    847.752.831.832.860.300.985.727.686.482.291.228.
    260.812.667.458.777.140.342.739.211.041

Sm67 = p3 * p18 * p105
397 * 

183783139772372071 * 

169207186381096030569641287629182352063847752831832860300985727686482291228260812667458777140342739211041

 1234567...68
2⁴
3
23
764.558.869
1.811.890.921
16.210.201.583.355.429.120.740.178.111.425.145.802.
   012.035.286.597
49.798.299.077.316.075.944.525.952.275.152.868.666.
   920.234.906.076.151.289

Sm68 = (p1)^4 * p1 * p2 * p9 * p10 * p50 * p56
2^4 * 
3 * 
23 * 
764558869 * 
1811890921 * 

16210201583355429120740178111425145802012035286597 * 

49798299077316075944525952275152868666920234906076151289

 1234567...69
3
13
23
8.684.576.204.660.284.317.187
281.259.608.597.535.749.175.083
15.490.495.288.652.004.091.050.327.089.107
3.637.485.176.043.309.178.386.946.614.318.767.365.
  372.143.115.591

Sm69 = p1 * p2 * p2 * p22 * p24 * p32 * p49
3 * 
13 * 
23 * 

8684576204660284317187 * 

281259608597535749175083 * 

15490495288652004091050327089107 * 

3637485176043309178386946614318767365372143115591

 1234567...70
2
5
2.411.111
109.315.518.091.391.293.936.799
11.555.516.101.313.335.177.332.236.222.295.571.524.
   323
405.346.669.169.620.786.437.208.619.979.711.016.226.
    055.320.437.594.464.205.451

Sm70 = p1 * p1 * p7 * p24 * p41 * p60
2 * 
5 * 
2411111 * 

109315518091391293936799 * 

11555516101313335177332236222295571524323 * 

405346669169620786437208619979711016226055320437594464205451

 1234567...71
3²
83
2.281
7.484.379.467.407.391.660.418.419.352.839
96.808.455.591.058.960.266.687.738.381.050.176.698.
   103.277.406.505.724.847.082.994.829.643.349.780.
   363.432.993.640.165.860.627

Sm71 = (p1)^2 * p2 * p4 * p31 * p95
3^2 * 
83 * 
2281 * 

7484379467407391660418419352839 * 

96808455591058960266687738381050176698103277406505724847082994829643349780363432993640165860627

 1234567...72
2²
3²
5.119
596.176.870.295.201.674.946.617.769
1.123.704.769.960.650.101.739.921.630.151.581.054.
  522.510.738.566.183.226.239.911.321.871.780.637.
  830.758.881.774.623.162.921.434.662.407

Sm72 = (p1)^2 * (p1)^2 * p4 * p27 * p103
2^2 * 
3^2 * 
5119 * 

596176870295201674946617769 * 

1123704769960650101739921630151581054522510738566183226239911321871780637830758881774623162921434662407

 1234567...73  (by Philippe Strohl)
37.907
1.612.352.371.081.094.864.112.011.094.480.307.952.
  600.705.089
201.992.666.185.187.831.800.817.490.810.938.117.880.
    341.395.186.600.971.262.233.773.863.756.955.874.
    363.353.778.851

Sm73 = p5 * p46 * p87    ( Philippe Strohl )
37907 * 

1612352371081094864112011094480307952600705089 * 

201992666185187831800817490810938117880341395186600971262233773863756955874363353778851
Factor p46 Sm73 by GMP-ECM

Sm73 = 37907.p46.p87

None of these factors could have been found by P-1 or P+1 with B1<10^14 and I was lucky

enough to catch the p46 with a ECM B1 of 10^6.

The group order of the curve is very smooth (B1=620227 and B2=1473569 are enough).

325683354264679693500307906698027336176043019186246110832678756888/

805244789707561834881407263896785700945962383243895973215176272739 (132 digits)

Using B1=2000000, B2=5000000, polynomial x^6, sigma=2799427343

Step 1 took 181065ms

********** Factor found in step 1: 1612352371081094864112011094480307952600705089

Found probable prime factor of 46 digits: 1612352371081094864112011094480307952600705089

Probable prime cofactor 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851

has 87 digits (both proven prime by S. Tomabechi APR-CL part of p_1 program)

 1234567...74
2
3
7
1.788.313
21.565.573
99.014.155.049.267.797.799
1.634.187.291.640.507.800.518.363
1.981.231.397.449.722.872.290.863.561.307
2.377.534.541.508.613.492.655.260.491.688.014.802.
  698.908.815.817

Sm74 = p1 * p1 * p1 * p7 * p8 * p20 * p25 * p31 * p49
2 * 
3 * 
7 * 
1788313 * 
21565573 * 

99014155049267797799 * 

1634187291640507800518363 * 

1981231397449722872290863561307 * 

2377534541508613492655260491688014802698908815817

 1234567...75  (by Sean A. Irvine)
3
5²
193.283
38.824.496.309.870.038.690.197.243.565.592.769.246.
   963.314.017
219.358.378.032.318.168.161.320.006.998.916.878.634.
    145.966.511.629.131.235.131.312.083.699.783.021.
    949.850.982.403

Sm75 = p1 * (p1)^2 * p6 * p47 * p87    ( Sean A. Irvine )
3 * 
5^2 * 
193283 * 

38824496309870038690197243565592769246963314017 * 

219358378032318168161320006998916878634145966511629131235131312083699783021949850982403

 1234567...76
2³
828.699.354.354.766.183
213.643.895.352.490.047.310.058.981
8.716.407.028.594.814.374.740.596.028.898.426.313.
  034.395.366.012.872.513.707.917.231.855.753.694.
  435.270.081.076.237.925.828.389

Sm76 = (p1)^3 * p18 * p27 * p97
2^3 * 

828699354354766183 * 

213643895352490047310058981 * 

8716407028594814374740596028898426313034395366012872513707917231855753694435270081076237925828389

 1234567...77
3
383.481.022.289.718.079.599.637
874.911.832.937.988.998.935.021
164.811.751.226.239.402.858.361.187.055.939.797.929
7.442.132.227.048.590.901.854.639.419.294.226.672.
  231.934.035.068.486.536.423

Sm77 = p1 * p24 * p24 * p39 * p58
3 * 

383481022289718079599637 * 

874911832937988998935021 * 

164811751226239402858361187055939797929 * 

7442132227048590901854639419294226672231934035068486536423

 1234567...78  (by Sean A. Irvine)
2
3
31
185.897
205.155.431.830.422.787.082.756.234.197.593.935.249.
    202.704.547.671.264.423
17.403.902.113.720.391.120.287.411.398.887.911.225.
   298.966.708.915.583.006.414.519.403.038.472.992.
   542.973.083

Sm78 = p1 * p1 * p2 * p6 * p57 * p83    ( Sean A. Irvine )
2 * 
3 * 
31 * 
185897 * 

205155431830422787082756234197593935249202704547671264423 * 

17403902113720391120287411398887911225298966708915583006414519403038472992542973083

 1234567...79
73
137
22.683.534.613.064.519.783
132.316.335.833.889.742.191.773
35.488.612.864.124.533.038.957.177.977
11.589.330.059.060.921.218.833.486.882.285.427.414.
   280.233.987.959.540.582.909.167.514.265.308.253

Sm79 = p2 * p3 * p20 * p24 * p29 * p74
73 * 
137 * 

22683534613064519783 * 

132316335833889742191773 * 

35488612864124533038957177977 * 

11589330059060921218833486882285427414280233987959540582909167514265308253

 1234567...80
2²
3³
5
101
10.263.751
1.295.331.340.195.453.366.408.489
1.702.600.917.839.548.328.745.392.482.587.491.026.
  230.318.172.323.434.581.398.602.992.701.169.952.
  537.157.469.971.305.061.091.390.839.579.932.352.
  102.383

Sm80 = (p1)^2 * (p1)^3 * p1 * p3 * p8 * p25 * p115
2^2 * 
3^3 * 
5 * 
101 * 
10263751 * 

1295331340195453366408489 * 

1702600917839548328745392482587491026230318172323434581398602992701169952537157469971305061091390839579932352102383

 1234567...81
3³
509
152.873.624.211.113.444.108.313.548.197
58.762.581.888.644.185.603.361.112.342.786.137.599.
   799.640.821.735.382.180.404.307.223.995.625.796.
   855.706.598.141.292.123.658.134.092.320.545.833.
   186.103.011

Sm81 = (p1)^3 * p3 * p30 * p119
3^3 * 
509 * 

152873624211113444108313548197 * 

58762581888644185603361112342786137599799640821735382180404307223995625796855706598141292123658134092320545833186103011

 1234567...82
2
29
4.703
10.091
12.295.349.967.251.726.424.104.854.676.730.107
334.523.571.229.968.373.890.203.385.137.399.026.475.
    051
1.090.461.105.551.993.653.223.776.199.179.348.475.
  393.504.023.636.425.991.597.284.018.461.539

Sm82 = p1 * p2 * p4 * p5 * p35 * p42 * p70
2 * 
29 * 
4703 * 
10091 * 

12295349967251726424104854676730107 * 

334523571229968373890203385137399026475051 * 

1090461105551993653223776199179348475393504023636425991597284018461539

 1234567...83  (by Sean A. Irvine)
3
53
503
177.918.442.980.303.859
21.875.480.270.521.598.141.087.357.354.188.092.945.
   840.550.359.281.483
3.966.169.790.267.211.790.412.249.283.896.602.109.
  358.687.165.012.835.285.295.541.472.324.348.526.
  743.126.307

Sm83 = p1 * p2 * p3 * p18 * p53 * p82    ( Sean A. Irvine )
3 * 
53 * 
503 * 

177918442980303859 * 

21875480270521598141087357354188092945840550359281483 * 

3966169790267211790412249283896602109358687165012835285295541472324348526743126307
by SNFS, 8 days


 1234567...84
2⁵
3
128.600.821.980.325.136.890.793.456.450.022.106.587.
    763.153.419.719.076.284.732.850.389.416.045.981.
    702.547.359.113.015.678.672.244.328.809.985.375.
    641.941.298.506.955.072.611.638.268.203.924.769.
    581.335.2379

Sm84 = (p1)^5 * p1 * p157

2^5 * 

3 * 

1286008219803251368907934564500221065877631534197190762847328503894160459817025473591130156786722443288099853756419412985069550726116382682039247695813352379

 1234567...85  (by Sean A. Irvine)
5
7²
120.549.814.855.596.987.772.827.562.271.063.563.633.
    851.059
2.112.809.210.944.968.177.871.685.727.287.164.545.
  437.750.155.430.310.661
197.843.626.412.162.026.434.764.405.036.310.959.588.
    059.884.460.495.810.550.047

Sm85 = p1 * (p1)^2 * p45 * p55 * p60    ( Sean A. Irvine )

5 * 

7^2 * 

120549814855596987772827562271063563633851059 * 

2112809210944968177871685727287164545437750155430310661 * 

197843626412162026434764405036310959588059884460495810550047
Sm85 C158 =

120549814855596987772827562271063563633851059 (p45) *

Using B1=11000000, sigma=1708124291

2112809210944968177871685727287164545437750155430310661 (p55) *

197843626412162026434764405036310959588059884460495810550047 (p60)

by GNFS, 1 day

 1234567...86  (by Sean A. Irvine)
2
3
23
1.056.149
718.252.229.986.396.496.762.902.999.331.863.301.257
10.828.687.641.092.318.839.822.035.841.363.590.407.
   263.202.742.239.027.773
1.089.075.252.400.674.157.091.531.724.111.232.381.
  528.208.779.232.955.680.665.273

Sm86 = p1 * p1 * p2 * p7 * p39 * p56 * p61    ( Sean A. Irvine )

2 * 

3 * 

23 * 

1056149 * 

718252229986396496762902999331863301257 * 

10828687641092318839822035841363590407263202742239027773 * 

1089075252400674157091531724111232381528208779232955680665273
Sm86 C154 =

718252229986396496762902999331863301257 (p39) * C116

Using B1=11000000, sigma=3414478964

10828687641092318839822035841363590407263202742239027773 (p56) *

1089075252400674157091531724111232381528208779232955680665273 (p61)

by GNFS, 2 days.

 1234567...87  (by Sean A. Irvine)
3
7
231.330.259
4.275.444.601
101.784.611.215.757.903.569.658.774.280.830.604.745.
    279.416.597.473
58.398.250.025.786.270.255.235.847.423.735.930.777.
   973.447.337.337.804.788.906.368.149.837.276.410.
   666.257.137.526.766.841.721

Sm87 = p1 * p1 * p9 * p10 * p51 * p95    ( Sean A. Irvine )

3 * 

7 * 

231330259 * 

4275444601 * 

101784611215757903569658774280830604745279416597473 * 

58398250025786270255235847423735930777973447337337804788906368149837276410666257137526766841721
Sm87 C145 = (p51) * (p95)

by SNFS, 14 days.

 1234567...88  (by Sean A. Irvine)
2²
12.414.068.351.873
462.668.377.429.470.430.246.269.302.055.630.668.010.
    673
144.494.999.796.935.291.164.027.251.780.366.969.508.
    458.166.480.331
3.718.931.833.006.826.909.360.514.481.439.595.803.
  175.244.655.637.881.136.348.103

Sm88 = (p1)^2 * p14 * p42 * p51 * p61    ( Sean A. Irvine )
2^2 * 

12414068351873 * 

462668377429470430246269302055630668010673 * 

144494999796935291164027251780366969508458166480331 * 

3718931833006826909360514481439595803175244655637881136348103
Sm88 C153=

462668377429470430246269302055630668010673 (p42)

B1=11000000, sigma=1512552247

144494999796935291164027251780366969508458166480331 (p51) *

3718931833006826909360514481439595803175244655637881136348103 (p61)

by GNFS, 8 hours

 1234567...89  (by Sean A. Irvine)
3²
13
31
97
163.060.459
789.841.356.493.369.879
496.118.159.817.126.721.484.175.235.476.073
26.459.905.787.227.421.825.352.754.831.024.262.009.
   257
2.075.552.579.046.417.801.880.667.285.191.357.553.
  672.027.185.826.871.770.761.977.511

Sm89 = (p1)^2 * p2 * p2 * p2 * p9 * p18 * p33 * p41 * p64    ( Sean A. Irvine )

3^2 * 

13 * 

31 * 

97 * 

163060459 * 

789841356493369879 * 

496118159817126721484175235476073 * 

26459905787227421825352754831024262009257 * 

2075552579046417801880667285191357553672027185826871770761977511

 1234567...90  (by Sean A. Irvine)
2
3²
5
1.987
179.827
2.166.457
5.469.640.487.155.071.172.064.105.436.159.054.827.
  205.011.884.517.193.846.381.587.779.057
323.974.513.721.871.489.318.385.733.207.245.357.406.
    204.798.917.206.286.895.918.649.972.193.592.038.
    458.818.136.011

Sm90 = p1 * (p1)^2 * p1 * p4 * p6 * p7 * p67 * p87    ( Sean A. Irvine )

2 * 

3^2 * 

5 * 

1987 * 

179827 * 

2166457 * 

5469640487155071172064105436159054827205011884517193846381587779057 * 

323974513721871489318385733207245357406204798917206286895918649972193592038458818136011
Sm90 C154=

(p67) * (p87)

by SNFS, 32 days

Submitted on Monday October 24, 2005 22:51

 1234567...91  (by Sean A. Irvine)
37
607
5.713.601.747.802.353
100.397.446.615.566.314.002.487
3.581.874.457.050.057.021.838.729.610.409.482.762.
  969.149.632.972.915.379
267.535.593.139.950.330.755.907.265.689.770.024.664.
    090.795.106.497.661.308.268.157.342.396.003.221

Sm91 = p2 * p3 * p16 * p24 * p55 * p75    ( Sean A. Irvine )

37 * 

607 * 

5713601747802353 * 

100397446615566314002487 * 

3581874457050057021838729610409482762969149632972915379 * 

267535593139950330755907265689770024664090795106497661308268157342396003221
Sm91 C129=

(p55) * (p75)

by GNFS, 4 days

Submitted on Monday October 24, 2005 22:51

 1234567...92
2³
3
75.503
46.731.404.628.893.905.607.210.235.741.707  ( 'p32' by Sean A. Irvine)
17.357.685.121.487.530.272.314.084.020.479.969.142.
   526.171.001.787.819.150.223.751.641
839.921.864.959.969.600.234.341.350.615.454.280.584.
    339.900.783.049.158.479.018.433.912.354.703

Sm92 = (p1)^3 * p1 * p5 * p32 * p65 * p72    ( Sean A. Irvine )

2^3 * 

3 * 

75503 * 

46731404628893905607210235741707 * 

17357685121487530272314084020479969142526171001787819150223751641 * 

839921864959969600234341350615454280584339900783049158479018433912354703
Sm92 C137=

(p65) * (p72)

by GNFS, 9 days

Submitted on Sunday January 22, 2006 21:28

 1234567...93
3
73
1.051
3.298.142.203
19.544.056.951.015.647.623.992.763.251  ( 'p29' by Sean A. Irvine)
4.886.013.639.051.371.332.965.225.321.191.263.200.
  785.903.705.285.317
1.703.057.751.798.522.700.187.996.077.196.637.285.
  517.155.003.415.445.664.199.429.017.748.369.723.
  643.706.497

Sm93 = p1 * p2 * p4 * p10 * p29 * p52 * p82    ( Sean A. Irvine )

3 * 

73 * 

1051 * 

3298142203 * 

19544056951015647623992763251 * 

4886013639051371332965225321191263200785903705285317 * 

1703057751798522700187996077196637285517155003415445664199429017748369723643706497
Sm93 C133=

(p52) * (p82)

by GNFS, 5 days

Submitted on Monday February 20, 2006 23:01

 1234567...94  (by Greg Childers)
2
12.871.181
98.250.285.823
1.825.097.233.762.709.447.432.521.941.926.649.289.
  213.154.260.264.910.537.140.594.516.431.173.070.
  300.371
2.674.525.573.684.858.697.560.701.870.658.348.933.
  916.102.325.593.721.165.422.426.453.989.766.526.
  938.215.889

Sm94 = p1 * p8 * p11 * p79 * p82    ( Greg Childers )

2 * 

12871181 * 

98250285823 * 

1825097233762709447432521941926649289213154260264910537140594516431173070300371 * 

2674525573684858697560701870658348933916102325593721165422426453989766526938215889
Summary for Sm94(c160) = p79 * p82

The factorization was completed using SNFS. GGNFS was used for the sieving

and msieve for the post-processing.

Submitted on Sun, 9 Dec 2007 11:27



 1234567...95  (by Sean A. Irvine)
3
5
7
401
244.987.542.265.129.586.458.446.183.157.595.351
119.684.333.324.585.760.380.296.925.278.736.677.052.
    991.667.067.598.465.535.119.086.641.122.308.977.
    254.652.550.763.964.697.554.302.296.677.991.161.
    440.001.789.403.458.655.109.609.795.769

Sm95 = p1 * p1 * p1 * p3 * p36 * p141    ( Sean A. Irvine )

3 * 

5 * 

7 * 

401 * 

244987542265129586458446183157595351 * 

119684333324585760380296925278736677052991667067598465535119086641122308977254652550763964697554302296677991161440001789403458655109609795769


 1234567...96
2²
3
23
60.331
7.414.218.343.605.898.007.054.904.008.539.678.229.
  463.872.328.651.811.494.111.562.828.507.144.051.
  357.405.695.052.612.835.346.584.059.319.708.614.
  758.837.877.621.899.193.657.692.066.488.505.067.
  022.654.601.125.869.790.297.498.349.041

Sm96 = (p1)^2 * p1 * p2 * p5 * p175

2^2 * 

3 * 

23 * 

60331 * 

7414218343605898007054904008539678229463872328651811494111562828507144051357405695052612835346584059319708614758837877621899193657692066488505067022654601125869790297498349041


 1234567...97
13
949.667.608.470.093.318.578.167.063.015.547.864.032.
    712.517.561.002.409.487.257.972.106.456.954.941.
    803.426.651.911.500.396.348.881.197.366.045.850.
    894.335.742.820.591.305.439.790.288.275.136.759.
    985.244.833.729.682.214.530.699.379.184.227.669

Sm97 = p2 * p183

13 * 

949667608470093318578167063015547864032712517561002409487257972106456954941803426651911500396348881197366045850894335742820591305439790288275136759985244833729682214530699379184227669


 1234567...98  (by Philippe Strohl)
2
3²
23
37
199 
1.495.444.452.918.817
381.502.754.125.464.943.168.932.369.122.248.696.781
3.588.472.635.471.667.861.938.967.869.443.938.442.
  910.813.342.994.227.048.889
197.825.482.406.769.698.151.783.117.995.020.967.519.
    766.027.202.915.861.687.264.259.155.363

Sm98 = p1 * (p1)^2 * p2 * p2 * p3 * p16 * p39 * p58 * p69    ( Philippe Strohl )

2 * 

3^2 * 

23 * 

37 * 

199 * 

1495444452918817 * 

381502754125464943168932369122248696781 * 

3588472635471667861938967869443938442910813342994227048889 * 

197825482406769698151783117995020967519766027202915861687264259155363


 1234567...99
3²
31.601
786.576.340.181
551.862.346.576.034.156.243.063.167.468.244.517.393.
    432.552.581.164.203.918.315.637.397.482.572.401.
    640.968.810.713.439.341.722.788.097.837.944.871.
    160.295.989.176.191.962.400.702.736.029.965.381.
    746.872.246.341.682.258.769.031 = c171

Sm99 = (p1)^2 * p5 * p12 * c171

3^2 * 

31601 * 

786576340181 * 

551862346576034156243063167468244517393432552581164203918315637397482572401640968810713439341722788097837944871160295989176191962400702736029965381746872246341682258769031

Please doublecheck the correctness of the above results before using them for continuing the search!




Sm100 (COMPLETE) by Sean A. Irvine

2^2
5^2
7^3
8171
1065829
2824782749 (p10)
20317177407273276661 (p20)
970447246795177523033247400823 (p30)
7420578382899399028284464392651452937744039836185355778662961413780805734369643748805299589898776112/
804950234221784569 (p118)


Sm108 (COMPLETE) by Sean A. Irvine

2^2
3^3
128451681010379681 (p18)
132761751746390611923240080737166083 (p36)
6703142557817928040555348648900674233695375904983084080935101634841300766484581974276898497657520542/
6833399525010462614317613333284615639359796130220299502987337 (p161)


Sm116 (COMPLETE) by Sean A. Irvine

2^2
3^2
2239
9787002048140152171263515060558503699 (p37)
1564979683672455156550590564550896170739590132221492657705868045238053081655725205100502721369811982/
50507087284878063256342705928229557508508670247743582143974583381133763456377474127925121483818271 (p198)


Sm121 (COMPLETE) by Sean A. Irvine

278240783 (p9)
105299178204417486675841093021769 (p33)
4213754301973277818574830150933029703205115128282586723382785882706969263182976786615125991432774212/
6655712800813928005415583544197992453104126217919256625510887081121101381586161564163756343745220847/
88731721938623 (p214)


Sm148 (COMPLETE) by Sean A. Irvine

2^2
197
11927
17377
273131
623321
3417425341307 (p13)
4614988413949 (p13)
8817212782626223819399721069204897 (p34)
3193000701568524782467188898304641220775712837053116231323237434768208956576768718690200934704769644/
9776432217795787176033049303491281548912080640497966801122571925082634457098946350721137505551941519/
011986808243341521869976182605502561225915860092642869 (p254)


Sm152 (COMPLETE) by Sean A. Irvine

2^4
3^2
131
10613
29354379044409991753 (p20)
2587833772662908004979 (p22)
4103096315830350734534473515557 (p31)
12805089500421274253268517941967 (p32)
17815076027044127272632744936161 (p32)
8672648427724666836335878649605123533671234498113722493001839423884394310675246313883662523667972796/
2252207354099527091658621300178181661297993537192234834905032751669182605720711181867690701061985005/
06817 (p205)


Sm165 (COMPLETE) by Sean A. Irvine

3
5
7
13
31
247007767 (p9)
490242053931613 (p15)
13183356310254866666237435750357 (p32)
1827567681941731356121062274519777291863760972834724140109364732283149431121763995026237820114303681/
5496592791501562871236022199555066011298451642231401735631929300761746199878863922607830081439132951/
8357914807533066417404260975659341568447505060701439696780455579283391217843114550193398184405873168/
7369979309788684753888188553 (p328)


Sm184 (COMPLETE) by Sean A. Irvine

2^4
7
59
191
1093
1223
22521973429 (p11)
15219125459582087 (p17)
158906425126963139 (p18)
2513521443592870099 (p19)
677008100402429325901609057 (p27)
7894977574571781556444786202593614139721506720817604366015528775760676373160442530345019483307700978/
5930092303778152032404551795675090170923053660293230843498614359663939844365627366165832785305317365/
4182408958317242742517820581180854453052925226658686768857580470091786086406610221754789129568203967/
384451608838167466879488313009807568569387 (p342)


Sm187 (COMPLETE) by Sean A. Irvine

349
506442073 (p9)
1080829169904060835770214147747 (p31)
6462532135259365632021314942658431728094733620599149141734327082367671298692320282350900597278296365/
5379540884023312710555856177308446767405172970938977772676796780228431702242816509113421339444592236/
2621714833233212554723714564174418111669498936207951085298551799080803363445759267522417246541605647/
9089775584237803310812087978174533031535543826808011950270774768093377786126458352214138913849333920/
84296657173 (p411)


Sm195 (COMPLETE) by Sean A. Irvine

3
5
397
21728563
300856949 (p9)
554551531 (p9)
8174619091 (p10)
165897663095213559529993681 (p27)
4216891792160044902686705799521388925390732888122432608757782570720072408665875338945809590873483499/
4620499297336767795766591884079938389340512146288914907796490815205714454677249295016313996731519073/
1294500128685930803732434591580562083296784964092846142348549703545534554252170080984646226664593569/
3244989301840859149448482745301257117142121991254187915811979621816086743861383233522991211424294391/
495728519167 (p412)

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