HOME plateWON | World!OfNumbers Normal Smarandache Concatenated NumbersPrime factors from 1 upto n (n=2,3,...,200) Reversed Smarandache Concatenated Numbers Repunits Factorization

Itinerary

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sm_N if N less than 118 - complete factorization is given on this page if N is above 117 - refer for the complete factorization to M. Fleuren page smallest Sm with unknown factors Sm with unknown factors (ref. M. Fleuren's page) Sm with new complete factorization : see list at end of page Sm with a new factor but still incomplete : consult Messages section Sm is prime (smallest one > Sm344869 ref. E. Weisstein)!

Prefatory Notes & Sources

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 = 118.
If there is a breaktrough in partially or completely factorising Sm118, 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 factors by Micha Fleuren
Primes by Listing by Carlos Rivera
Consecutive Number Sequences by Eric W. Weisstein
Smarandache Sequences by Eric W. Weisstein
Smarandache Prime 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 (email) from Bucharest)

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

OEIS entries

A007908 - Concatenation of the numbers from 1 to n.
A046460 - Number of prime factors of concatenation of numbers from 1 up to n, with multiplicity.
A046461 - Numbers n such that concatenation of numbers from 1 to n is a semiprime.
A046462 - Concatenation of numbers from 1 to a(n) has exactly 3 prime factors, with multiplicity.
A046463 - Concatenation of numbers from 1 to a(n) has exactly 4 prime factors, with multiplicity.
A046464 - Concatenation of numbers from 1 to a(n) has exactly 5 prime factors, with multiplicity.
A046465 - Concatenation of numbers from 1 to a(n) has exactly 6 prime factors, with multiplicity.
A046466 - Concatenation of numbers from 1 to a(n) has exactly 7 prime factors, with multiplicity.
A046467 - Concatenation of numbers from 1 to a(n) has exactly 8 prime factors, with multiplicity.
A046468 - Concatenation of numbers from 1 to a(n) has exactly 9 prime factors, with multiplicity.
A048342 - Numbers n such that the concatenation of the numbers 1, 2, ..., n is a product of distinct primes.
A050675 - Numbers n such that concatenation of numbers from 1 to n is a powerful(1) number.
A050676 - Let b(n) = number of prime factors (with multiplicity) of concatenation of numbers from 1 to n; sequence gives smallest number m with b(m) = n.

PrimeForm or PFGW

To calculate the length of a Smarandache number in PrimeForm you just enter at the prompt
pfgw64 -od -f0 -q"len(Sm(119))"
For the reversed Smarandache number you type
pfgw64 -od -f0 -q"len(Smr(119))"

Some Factorization Websites

Messages

[ April 25, 2015 ]
Stephen Tucker's (email) search for prime Smarandache numbers !

Dear Patrick,
I have found your list of Smaradache factors and noticed that no prime Smarandache number
has been found yet. Well, I decided to try looking for one.
Using Dario Alpern's ECM Factorizing applet, (and software I wrote myself to generate the numbers),
I have discovered that there are no prime Smarandache numbers less than Sm2659.
When I tried using Dario's applet to factorize Sm2659 (which, by the way, has no factors less than
or equal to 39989) the applet's attempt to start the Prime Check routine stalled.
I tried using it to check Sm2713, but the same thing happened again.
Dario's website does stipulate a maximum length of input number of 10000 digits. However, Sm2659
is "only" 9529 digits long, so perhaps his stated limit of 10000 is rounded up.
After a brief search on the web, I haven't discovered anything about prime Smaradanche numbers.
I wonder if it could be that a Smaradanche number cannot be prime.

Hope this is of interest.

Yours,
Stephen Tucker (UK).

Eric Weisstein [ http://mathworld.wolfram.com/ConsecutiveNumberSequences.html ]
wrote he extended the search up to 38712 terms which is
quite ahead of your Sm2659. He did find a probable prime for
the reversed case though (Rsm37765).

Note Primeform with the program PFGW64.EXE has a built-in command
Sm(x) and Smr(x) to search for (probable) primes directly.
I did a run up to Sm(10000) and found indeed none. For larger
values one needs a faster computer than I have at the moment.
So there is still opportunity to detect the first PRP Sm !

[ May 20, 2008 ]
Greg Childers (email) factorized Sm99 ! [ go to entry ]

Hi Patrick,

I finally got around to factoring Sm99 by SNFS. As for Sm94, I used
the GGNFS lattice siever and msieve for the postprocessing. The factors are

P65: 37726668883887938032416757819314355053940153680075342644295667759

P107: 14627910783072606795565990651314126145674770336615677946549896262532933945988541999815567058347827465728809

Greg

[ December 9, 2007 ]
Greg Childers (email) factorized Sm94 ! [ go to 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 ! [ go to 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 ! [ go to 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 ! [ go to 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 = semiprime
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  (by Greg Childers)
32
31.601
786.576.340.181
37.726.668.883.887.938.032.416.757.819.314.355.053.
940.153.680.075.342.644.295.667.759
14.627.910.783.072.606.795.565.990.651.314.126.145.
674.770.336.615.677.946.549.896.262.532.933.945.
988.541.999.815.567.058.347.827.465.728.809

Sm99 = (p1)^2 * p5 * p12 * p65 * p107 [ Length = 189 ]    ( Greg Childers )
3^2 *
31601 *
786576340181 *
37726668883887938032416757819314355053940153680075342644295667759 *
14627910783072606795565990651314126145674770336615677946549896262532933945988541999815567058347827465728809

Summary for Sm99(c177) = p65 * p107
I finally got around to factoring Sm99 by SNFS. As for Sm94, I used
the GGNFS lattice siever and msieve for the postprocessing.
Submitted on Tue, 20 May 2008 4:35

1234567...100  (by Sean A. Irvine)
22
52
73
8.171
1.065.829
2.824.782.749
20.317.177.407.273.276.661
970.447.246.795.177.523.033.247.400.823
7.420.578.382.899.399.028.284.464.392.651.452.937.
744.039.836.185.355.778.662.961.413.780.805.734.
369.643.748.805.299.589.898.776.112.804.950.234.
221.784.569

Sm100 = (p1)^2 * (p1)^2 * (p1)^3 * p4 * p7 * p10 * p20 * p30 * p118 [ Length = 192 ]    ( Sean A. Irvine )
2^2 *
5^2 *
7^3 *
8171 *
1065829 *
2824782749 *
20317177407273276661 *
970447246795177523033247400823 *
7420578382899399028284464392651452937744039836185355778662961413780805734369643748805299589898776112804950234221784569

1234567...101  (by Bob Backstrom)
3
8.377
799.917.088.062.980.754.649
1.399.463.086.740.105.394.672.913.130.945.493.026.
937.913.499.238.148.790.743.003
4.388.325.012.701.307.167.526.588.635.576.876.644.
759.452.668.196.597.056.747.408.345.988.387.366.
211.263.062.577.487.913.664.612.635.611.915.493

Sm101 = p1 * p4 * p21 * p61 * p109 [ Length = 195 ]    ( Bob Backstrom )
3 *
8377 *
799917088062980754649 *
1399463086740105394672913130945493026937913499238148790743003 *
4388325012701307167526588635576876644759452668196597056747408345988387366211263062577487913664612635611915493

Summary for Sm101(c169) = p61 * p109
Hello Patrick,
Here's another wanted number for your tables:
Sm(101) = 3 * 8377 * 799917088062980754649 * C169
Tue Jun  5 01:18:11 2012  prp61 factor: 1399463086740105394672913130945493026937913499238148790743003
Tue Jun  5 01:18:11 2012  prp109 factor: 4388325012701307167526588635576876644759452668196597056747408345988387366211263062577487913664612635611915493
Tue Jun  5 01:18:11 2012  elapsed time 04:27:08
(Just the elapsed time for ONE sqrt - it only took one, luckily).
The whole number took many weeks on various machines. The relations were slow coming because the Snfs coefficients were pretty dreadful
as you can see from the Msieve log below.
Mon Jun  4 20:51:03 2012  Msieve v. 1.44
Mon Jun  4 20:51:03 2012  random seeds: 4714fab8 a98d82fd
Mon Jun  4 20:51:03 2012  factoring
6141298867893783540378996188437492127764003798590081909642744192552148805391571094462286943973793319/
310495244779697771718230720369645297842348701438176773337763517045479 (169 digits)
Mon Jun  4 20:51:04 2012  no P-1/P+1/ECM available, skipping
Mon Jun  4 20:51:04 2012  commencing number field sieve (169-digit input)
Mon Jun  4 20:51:04 2012  R0: -10000000000000000000000000000000000000
Mon Jun  4 20:51:04 2012  R1:  1
Mon Jun  4 20:51:04 2012  A0: -8919910099
Mon Jun  4 20:51:04 2012  A1:  0
Mon Jun  4 20:51:04 2012  A2:  0
Mon Jun  4 20:51:04 2012  A3:  0
Mon Jun  4 20:51:04 2012  A4:  0
Mon Jun  4 20:51:04 2012  A5:  12099999899800
Mon Jun  4 20:51:04 2012  skew 1.00, size 3.077673e-16, alpha -0.346420, combined = 6.775396e-13
Kind regards,
--Bob.
Submitted on Mon, 4 June 2012 18:44

1234567...102
2
3
19
89
3.607
15.887
32.993
2.865.523.753
2.245.981.950.884.772.863.770.930.273.540.385.579.
914.865.629.636.627.917.458.256.811.732.689.892.
492.870.743.326.877.749.976.350.147.897.124.023.
992.523.914.020.180.640.624.011.740.696.205.659.
507.665.744.332.920.411.510.673.767

Sm103 = p1 * p1 * p2 * p2 * p4 * p5 * p5 * p10 * p172 [ Length = 198 ]
2 *
3 *
19 *
89 *
3607 *
15887 *
32993 *
2865523753 *
2245981950884772863770930273540385579914865629636627917458256811732689892492870743326877749976350147897124023992523914020180640624011740696205659507665744332920411510673767

1234567...103  (by Sean A. Irvine)
131
1.231
1.713.675.826.579.469
16.908.963.624.339.537.484.508.436.321.314.327.604.
030.763.349.996.047.014.668.841.426.185.197
26.420.435.289.199.660.352.290.245.657.167.852.985.
476.641.946.070.651.819.895.933.156.168.339.498.
719.086.012.326.404.560.442.282.402.403.559.611

Sm103 = p3 * p4 * p16 * p71 * p110 [ Length = 201 ]    ( Sean A. Irvine )
131 *
1231 *
1713675826579469 *
16908963624339537484508436321314327604030763349996047014668841426185197 *
26420435289199660352290245657167852985476641946070651819895933156168339498719086012326404560442282402403559611

Summary for Sm103(c180) = p71 * p110
The factorization of the C180 after removal of the small factors was completed by SNFS using yafu.
The entire factorization took 6 months of otherwise idle time on a single 12-core machine.
Regards,
Sean A. Irvine
Submitted on Mon, 15 February 2016 10:46

1234567...104  (by Sean A. Irvine)
26
3
59
773
19.601.852.982.312.892.289
117.416.055.745.722.199.032.551.613.030.131.955.173.
140.365.000.320.768.767.578.421.207.867
6.125.726.861.692.155.074.440.026.231.293.274.444.
423.805.613.657.273.299.528.150.618.521.012.506.
340.221.515.290.231.138.888.396.870.065.232.607

Sm104 = (p1)^6 * p1 * p2 * p3 * p20 * p69 * p109 [ Length = 204 ]    ( Sean A. Irvine )
2^6 *
3 *
59 *
773 *
19601852982312892289 *
117416055745722199032551613030131955173140365000320768767578421207867 *
6125726861692155074440026231293274444423805613657273299528150618521012506340221515290231138888396870065232607
Summary for Sm104(c177) = p69 * p109
I completed the factorization of the remaining C177 of Sm104 by GNFS after 6 months of sieving
and 17 days linear algebra.
The entire computation was done with yafu running on a single 3.4 GHz i7-2600 machine.
Regards,
Sean A. Irvine
Submitted on Sat, 21 March 2020 2:18

1234567...105  (by Sean A. Irvine)
3
5
193
6.942.508.281.251
90.853.974.148.830.729.568.788.807.471.204.169.448.
373.857
67.609.243.102.773.972.838.875.424.854.217.967.300.
371.972.209.133.190.536.893.586.620.791.162.850.
744.838.052.281.507.779.485.845.273.498.264.830.
080.938.632.761.526.794.830.712.920.440.816.557

Sm105 = p1 * p1 * p3 * p13 * p44 * p146 [ length = 207 ]    ( Sean A. Irvine )
3 *
5 *
193 *
6942508281251 *
90853974148830729568788807471204169448373857 *
67609243102773972838875424854217967300371972209133190536893586620791162850744838052281507779485845273498264830080938632761526794830712920440816557
Hi Patrick,
It has been a long time between drinks, but I finally factored another of these numbers
Sm105(c190)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=982310399
Step 1 took 63945ms
Step 2 took 30405ms
********** Factor found in step 2: 90853974148830729568788807471204169448373857
Found probable prime factor of 44 digits: 90853974148830729568788807471204169448373857
Probable prime cofactor 67609243102773972838... ...94830712920440816557 has 146 digits
Sean.
Submitted on Wed, 22 Dec 2010 19:43

1234567...106  (by Sean A. Irvine)
2
11
127
827
95.383.501.607.400.293.616.004.374.931
54.259.599.094.002.572.583.355.411.045.946.413
375.159.085.605.310.877.928.459.072.269.605.386.653.
376.782.374.874.196.433.925.741.599.663
27.518.056.325.201.854.933.261.643.718.251.313.697.
576.510.084.474.601.978.478.694.683.051.383

Sm106 = p1 * p2 * p3 * p3 * p29 * p35 * p69 * p71 [ Length = 210 ]    ( Sean A. Irvine )
2 *
11 *
127 *
827 *
95383501607400293616004374931 *
54259599094002572583355411045946413 *
375159085605310877928459072269605386653376782374874196433925741599663 *
27518056325201854933261643718251313697576510084474601978478694683051383
by GNFS, 7 days
Finally did another of these numbers, sorry but it is not the most wanted Sm101.
Submitted on Wed, 29 Apr 2009 17:50

1234567...107
33
536.288.185.369
8.526.150.295.974.562.563.911.703.097.396.807.303.
361.305.853.752.080.385.827.103.422.281.006.173.
895.434.732.314.352.853.475.423.512.542.010.066.
856.002.013.066.381.244.223.149.688.686.332.747.
287.256.098.942.256.562.363.655.334.309.484.941.
298.623.600.483.738.889

Sm107 = (p1)^3 * p12 * p199 [ Length = 213 ]
3^3 *
536288185369 *
8526150295974562563911703097396807303361305853752080385827103422281006173895434732314352853475423512542010066856002013066381244223149688686332747287256098942256562363655334309484941298623600483738889

1234567...108  (by Sean A. Irvine)
22
33
128.451.681.010.379.681
132.761.751.746.390.611.923.240.080.737.166.083
67.031.425.578.179.280.405.553.486.489.006.742.336.
953.759.049.830.840.809.351.016.348.413.007.664.
845.819.742.768.984.976.575.205.426.833.399.525.
010.462.614.317.613.333.284.615.639.359.796.130.
220.299.502.987.337

Sm108 = (p1)^2 * (p1)^3 * p18 * p36 * p161 [ Length = 216 ]    ( Sean A. Irvine )
2^2 *
3^3 *
128451681010379681 *
132761751746390611923240080737166083 *
67031425578179280405553486489006742336953759049830840809351016348413007664845819742768984976575205426833399525010462614317613333284615639359796130220299502987337

1234567...109  (by ?)
7
1.559
78.176.687
73.024.355.266.099.724.939
9.943.216.978.062.352.390.003.139.833.531
1.330.054.388.136.326.845.371.542.874.560.114.721.
263.427.298.182.714.056.642.677.810.603
149.840.603.084.337.475.988.993.463.236.995.110.967.
352.586.095.183.241.932.010.459.722.363.567.237.
123.276.130.962.657

Sm109 = p1 * p4 * p8 * p20 * p31 * p67 * p90 [ Length = 219 ]    ( ? )
7 *
1559 *
78176687 *
73024355266099724939 *
9943216978062352390003139833531 *
1330054388136326845371542874560114721263427298182714056642677810603 *
149840603084337475988993463236995110967352586095183241932010459722363567237123276130962657

1234567...110
2
3
5
4.517
18.443.752.916.913.621.413
49.396.290.575.478.070.579.962.193.789.705.514.377.
113.696.579.391.181.438.562.209.557.211.046.308.
140.914.955.475.375.292.377.669.698.324.210.580.
411.428.837.724.109.733.589.770.430.705.239.901.
861.854.012.027.457.023.299.672.370.583.841.892.
589.110.518.827.197

Sm110 = p1 * p1 * p1 * p4 * p20 * p197 [ Length = 222 ]
2 *
3 *
5 *
4517 *
18443752916913621413 *
49396290575478070579962193789705514377113696579391181438562209557211046308140914955475375292377669698324210580411428837724109733589770430705239901861854012027457023299672370583841892589110518827197

1234567...111
3
293
431
230.273
209.071
241.423.723
3.182.306.131
171.974.155.987
1.532.064.083.461
59.183.601.887.848.987
8.526.805.649.394.145.853
27.151.072.184.008.709.784.271
2.440.480.034.289.871.822.370.862.693.886.835.126.
099.170.952.229.129.167.119.083.277.062.899.175.
394.632.300.484.951.689.048.576.681.026.896.223

Sm111 = p1 * p3 * p3 * p6 * p6 * p9 * p10 * p12 * p13 * p17 * p19 * p23 * p109 [ Length = 225 ]
3 *
293 *
431 *
230273 *
209071 *
241423723 *
3182306131 *
171974155987 *
1532064083461 *
59183601887848987 *
8526805649394145853 *
27151072184008709784271 *
2440480034289871822370862693886835126099170952229129167119083277062899175394632300484951689048576681026896223

1234567...112
23
16.619
449.797
894.009.023
74.225.338.554.790.133
10.021.106.769.497.255.963.093
3.104.515.050.823.723.908.076.909.137.590.343.647.
825.269.545.315.652.029.790.926.783.188.211.767.
084.523.827.184.031.625.338.265.911.008.653.113.
512.314.794.480.936.566.758.254.656.863.951.748.
098.953.803.988.065.923.879.729

Sm112 = (p1)^3 * p5 * p6 * p9 * p17 * p23 * p169 [ Length = 228 ]
2^3 *
16619 *
449797 *
894009023 *
74225338554790133 *
10021106769497255963093 *
3104515050823723908076909137590343647825269545315652029790926783188211767084523827184031625338265911008653113512314794480936566758254656863951748098953803988065923879729

1234567...113  (by Sean A. Irvine)
3
11
13
5.653
1.016.453
16.784.357
116.507.891.014.281.007
6.844.495.453.726.387.858.061.775.603.297.883.751
274.083.639.473.114.418.810.098.845.553.160.469.060.
803.472.020.901.711.735.885.001.850.493.035.179
13.652.330.611.204.925.298.260.606.291.932.608.056.
492.271.043.478.425.764.831.204.949.788.104.223.
444.207.523

Sm113 = p1 * p2 * p2 * p4 * p7 * p8 * p18 * p37 * p75 * p83 [ Length = 231 ]    ( Sean A. Irvine )
3 *
11 *
13 *
5653 *
1016453 *
16784357 *
116507891014281007 *
6844495453726387858061775603297883751 *
274083639473114418810098845553160469060803472020901711735885001850493035179 *
13652330611204925298260606291932608056492271043478425764831204949788104223444207523
Summary for Sm113(c157) = p75 * p83
" The entire computation of Sm104(C157) was done with yafu running on a single 3.4 GHz i7-2600 machine ".
Further, I also factored the remaining C157 composite of Sm113 by GNFS in 1 month using a similar machine.
I believe Sm114 is next smallest unfactored number of this form.
Regards,
Sean A. Irvine
Submitted on Sat, 21 March 2020 2:18

1234567...114  (by Sean A. Irvine)
2
3
7
178.333
2.042.059.881.000.388.200.555.074.336.219
8.678.622.406.220.213.516.465.050.301.044.327
24.075.568.431.816.864.297.632.248.860.777.423.507.
383.641.907
62.041.046.777.207.692.242.447.572.091.924.037.212.
783.315.235.431.589
622.671.572.255.303.237.737.485.133.617.360.962.819.
046.403.525.686.867.675.770.351

Sm114 = p1 * p1 * p1 * p6 * p31 * p34 * p47 * p53 * p63 [ Length = 234 ]    ( Sean A. Irvine )
2 *
3 *
7 *
178333 *
2042059881000388200555074336219 *
8678622406220213516465050301044327 *
24075568431816864297632248860777423507383641907 *
62041046777207692242447572091924037212783315235431589 *
622671572255303237737485133617360962819046403525686867675770351
Summary for Sm114(c162) = p47 * p53 * p63
"The third to last factor (47 digits) was found by ECM with b1=11e7, leaving an easy C116 by GNFS to finish it off."
Submitted on Wed, 29 April 2020 6:05

1234567...115  (by Sean A. Irvine)
5
17
19
41
36.607
71.518.987
283.858.194.594.979.819
35.876.849.722.942.437.286.649.396.513.492.746.925.
705.038.271.531
69.929.007.238.910.189.440.896.360.020.171.554.156.
771.275.344.878.594.027.300.265.571.638.084.469.
443.386.117.564.529.410.882.181.001.246.595.145.
982.221.865.975.563.979.407.080.860.715.180.311.
683.161

Sm115 = p1 * p3 * p3 * p3 * p5 * p8 * p18 * p50 * p152 [ Length = 237 ]    ( Sean A. Irvine )
5 *
17 *
19 *
41 *
36607 *
71518987 *
283858194594979819 *
35876849722942437286649396513492746925705038271531 *
69929007238910189440896360020171554156771275344878594027300265571638084469443386117564529410882181001246595145982221865975563979407080860715180311683161
Summary for Sm115(c202) = p50 * p152
GMP-ECM 6.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM]
Input number is 2508832483 ... 6758389491 (202 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1588162844
Step 1 took 1113195ms
Step 2 took 257537ms
********** Factor found in step 2: 35876849722942437286649396513492746925705038271531
Found probable prime factor of 50 digits: 35876849722942437286649396513492746925705038271531
Probable prime cofactor 6992900723 ... 0311683161 has 152 digits
Submitted on Sun, 8 November 2020 22:46

1234567...116  (by Sean A. Irvine)
22
32
2.239
9.787.002.048.140.152.171.263.515.060.558.503.699
156.497.968.367.245.515.655.059.056.455.089.617.073.
959.013.222.149.265.770.586.804.523.805.308.165.
572.520.510.050.272.136.981.198.250.507.087.284.
878.063.256.342.705.928.229.557.508.508.670.247.
743.582.143.974.583.381.133.763.456.377.474.127.
925.121.483.818.271

Sm116 = (p1)^2 * (p1)^2 * p4 * p37 * p198 [ Length = 240 ]    ( Sean A. Irvine )
2^2 *
3^2 *
2239 *
9787002048140152171263515060558503699 *
156497968367245515655059056455089617073959013222149265770586804523805308165572520510050272136981198250507087284878063256342705928229557508508670247743582143974583381133763456377474127925121483818271

1234567...117
32
31.883
333.699.561.211
28.437.086.452.217.952.631
29.899.433.706.805.424.728.763.564.400.367.447  ( 'p35' by Philippe Strohl)
319.505.907.958.401.958.357.051.507.462.193.336.760.
619
4.746.032.403.816.815.975.214.853.624.607.036.716.
257.319.634.142.438.753.425.546.024.369.121.494.
473.738.828.190.063.585.349.428.105.104.156.771.
415.393.005.556.040.837.247

Sm117 = (p1)^2 * p5 * p12 * p20 * p35 * p42 * p130 [ Length = 243 ]    ( Sean A. Irvine )
3^2 *
31883 *
333699561211 *
28437086452217952631 *
29899433706805424728763564400367447 *
319505907958401958357051507462193336760619 *
4746032403816815975214853624607036716257319634142438753425546024369121494473738828190063585349428105104156771415393005556040837247
Summary for p35 of Sm117
Philippe Strohl found a new factor of Sm117 (but the cofactor is still composite) :
Input number is (above) c206
Using B1=50000000, B2=288591693406, polynomial Dickson(12), sigma=759744520
dF=65536, k=6, d=690690, d2=17, i0=56
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
2	5	14	51	223	1139	6555	42004	296146	2292504
Step 1 took 1567405ms
Step 2 took 365869ms
********** Factor found in step 2: 29899433706805424728763564400367447
Found probable prime factor of 35 digits: 29899433706805424728763564400367447
Composite cofactor
1516385392381488800257172455421115218103131389426237636403907504872104848630821256747576627427151045/
955402969807173970504574397911322632329216437824800943241454211577975893 has 172 digits
Submitted on Friday 22/08/2008 14:59

Summary for Sm117(c172) = p42 * p130
Unexpectedly, the next one came out rather quick,  here is the rest of Sm117:
Run 657 out of 4590:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3332531727
Step 1 took 35672ms
Step 2 took 13620ms
********** Factor found in step 2: 319505907958401958357051507462193336760619
Found probable prime factor of 42 digits: 319505907958401958357051507462193336760619
Probable prime cofactor 4746032403 ... 6040837247 has 130 digits

Sean.
Submitted on Mon, 9 November 2020 10:42

1234567...118
2
83
33.352.084.523 (MF)
20.481.677.004.050.305.811 (MF)
1.088.725.496.688.995.065.917.555.290.398.211.742.
035.033.470.545.839.114.357.207.797.330.428.976.
086.992.860.487.685.496.852.884.467.613.284.688.
099.978.929.533.430.468.893.051.793.566.503.012.
287.207.422.945.984.682.148.992.628.368.919.209.
392.043.127.040.432.150.185.424.056.721.141 = c214

Sm118 = p1 * p2 * p11 * p20 * c214 [ Length = 246 ] )
2 *
83 *
33352084523 *
20481677004050305811 *
1088725496688995065917555290398211742035033470545839114357207797330428976086992860487685496852884467613284688099978929533430468893051793566503012287207422945984682148992628368919209392043127040432150185424056721141

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

```

In the Queue
```

1234567...119
3
59
101
139
2.801
17.737.500.810.197.818.073.272.016.530.327.479.006.
034.224.592.632.475.710.973.700.941.164.877.995.
756.223.660.197.285.056.038.943.431.164.782.790.
079.424.042.410.942.311.563.116.291.678.362.630.
605.443.361.422.347.301.284.854.160.351.578.178.
778.682.625.109.356.092.258.844.542.785.861.818.
452.104.859.596.299.949.073 = c239

Sm119 = p1 * p2 * p3 * p3 * p4 * c239 [ Length = 249 ] )
3 *
59 *
101 *
139 *
2801 *
17737500810197818073272016530327479006034224592632475710973700941164877995756223660197285056038943431164782790079424042410942311563116291678362630605443361422347301284854160351578178778682625109356092258844542785861818452104859596299949073

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)

```