all the prime factors of the smarandache concatenated numbers upto the first not factor

8/9/2019 All the prime factors of the Smarandache Concatenated Numbers upto the first not factor

http://slidepdf.com/reader/full/all-the-prime-factors-of-the-smarandache-concatenated-numbers-upto-the-first 1/32



NFSNET - Number Field Sieve GGNFS - A Number Field Sieve implementationGMP-ECM 6.0.1

Messages

[ 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 usedthe 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 sievedto 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 Smarandacheconcatenated number. It was a 126 digits composite.I have broken it with ggnfs (a wonderful program : I have done it witha common laptop computer with "only" 512 megs of ram and a 1.4 GHzceleron 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 =

of 32All the prime factors of the Smarandache Concatenated Numbers upto the first not factor ...

8/12/2010http://users.skynet.be/worldofnumbers/factorlist.htm



(p51) * (p95)by SNFS, 14 daysSm88 C153 =(p42) * (p51) * (p61)by GNFS, 8 hours

Sm90 looks like it will have to be SNFS since ECM has failedto 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* 2.3^2.23.37.199p16: 1495444452918817(MF)c165: 270825497607069872452415496119443135107702791840293286471110488510476827439126669519712057435717362779439193614301623544632857479569035194034142023605896434694145167

Line=16/32 Curves=47/1000 B1=1000000 factors=0C165 Using B1=1000000, B2=839549780, polynomial Dickson(6), sigma=594918519Step 1 took 28422msStep 2 took 18926ms********** Factor found in step 2: 381502754125464943168932369122248696781Found probable prime factor of 39 digits:381502754125464943168932369122248696781

Composite cofactor709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707 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 earlierI 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=17081242912112809210944968177871685727287164545437750155430310661 (p55) *197843626412162026434764405036310959588059884460495810550047 (p60)by GNFS, 1 day

Sm86 C154 =718252229986396496762902999331863301257 (p39) * C116Using B1=11000000, sigma=3414478964C116 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=1e6on all Sm(n), n <= 200)

Sm114 8678622406220213516465050301044327Sm159 45941358846148651407783221723920871719Sm171 40202471819457246557501649563881337Sm193 5167315927941164272437909427556797

Sean.

It seems that a fierce competition is going on. But to avoidduplicate work and loose valuable cpu time I advice stronglyto 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 byecm) and Sm86 (with a p39 and a ggnfs on the remaining c115)... Thisrepresents quite a large amount of cpu work. Sm84 factorization is stillknown 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 seenpreviously reported. All these were found with ECM B1=1e6.

Sm89 496118159817126721484175235476073Sm89 26459905787227421825352754831024262009257.P64Sm92 46731404628893905607210235741707Sm93 19544056951015647623992763251 Sm95 244987542265129586458446183157595351.P141Sm100 970447246795177523033247400823.P118Sm106 95383501607400293616004374931Sm106 54259599094002572583355411045946413 Sm108 132761751746390611923240080737166083.P161Sm109 9943216978062352390003139833531Sm114 2042059881000388200555074336219 Sm116 9787002048140152171263515060558503699.P198Sm121 105299178204417486675841093021769.P214Sm123 12347002211187670552593982429Sm123 2829927788416784955921382453753Sm125 295999706346724665505289Sm137 144065103514544138702103468451 Sm148 8817212782626223819399721069204897.P254Sm152 4103096315830350734534473515557Sm152 12805089500421274253268517941967Sm152 17815076027044127272632744936161.P205Sm154 32063206397901252963254536935569Sm159 11855111297257593607972759339201Sm160 64603936118676024484144135734907Sm162 22260247937572504750086047Sm164 1039418554780603268384723777072953 Sm165 13183356310254866666237435750357.P328Sm176 1011379313630785579015894871Sm183 553245689211853052761209813199 Sm184 677008100402429325901609057.P342Sm187 1080829169904060835770214147747.P411Sm193 419908232491384495189 Sm195 165897663095213559529993681.P412Sm198 14158849264684185910199571953

Further, after studying Backstrom's work on Rsm76 I am now able to generateSNFS polynomials for all the remaining Sm numbers below 100. It would havebeen much faster to do Sm78 by SNFS, but I had already started it beforeworking out how to apply SNFS to the number. It should be possible to completeall 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 completewith the discovery of a p46 by GMP-ECM...

Sm73 = 37907.p46.p87p46: 1612352371081094864112011094480307952600705089p87: 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851...Sm74 factorization is known and the next composite to challenge is Sm75with no factors expected below 35 digits...

Sm74 = 2.3.7.1788313.21565573.p20.p25.p31.p49p20: 99014155049267797799p25: 1634187291640507800518363(PZ)p31: 1981231397449722872290863561307p49: 2377534541508613492655260491688014802698908815817

Sm75* 3.5^2.193283.c133c133:851647853845481367839983983361331811035304896846801931077529055832/ 3936344974946612980172082837107906069172212808249295700548030242851

The List of Sm Factors

1

1

12

22

3

123

341

1234

2

617

Sm1 = p1 = unity

1

Sm2 = (p1)^2 * p1

2^2 *

3

Sm3 = p1 * p2 = semiprime

3 *

41


2 *





12345

3

5

823

123456

26

3

643

1234567

127

9.721

12345678

2

32

47

14.593

123456789

32

3.607

3.803

12345678910

2

5

1.234.567.891

1234567891011

3

7

13

67

107

630.803

617

Sm5 = p1 * p1 * p3

3 *

5 *

823

Sm6 = (p1)^6 * p1 * p3

2^6 *

3 *

643


127 *

9721

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

2 *

3^2 *

47 *

14593

Sm9 = (p1)^2 * p4 * p4

3^2 *

3607 *

3803

Sm10 = p1 * p1 * p102 *

5 *

1234567891





1234567...12

23

32.437

2.110.805.449

1234567...13

113

125.693

869.211.457

1234567...14

2

3

205.761.315.168.520.219

1234567...15

3

58.230.452.606.740.808.761

1234567...16

22

2.507.191.691

1.231.026.625.769

1234567...17

32

47

4.993

584.538.396.786.764.503

Sm11 = p1 * p1 * p2 * p2 * p3 * p6

3 *

7 *

13 *

67 *

107 *

630803

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

2^3 *

3 *

2437 *

2110805449

Sm13 = p3 * p6 * p9

113 *125693 *

869211457

Sm14 = p1 * p1 * p18

2 *

3 *

205761315168520219

Sm15 = p1 * p1 * p19

3 *

5 *

8230452606740808761

Sm16 = (p1)^2 * p10 * p13

2^2 *

2507191691 *

1231026625769

Sm17 = (p1)^2 * p2 * p4 * p18

3^2 *

47 *

4993 *

584538396786764503





1234567...18

2

32

97

88.241

801.309.546.900.123.763

1234567...19

13

43

79

281

1.193

833.929.457.045.867.563

1234567...20

25

3

5

323.339

3.347.983

2.375.923.237.887.317

1234567...21

3

17

37

43

103

131

140.453

802.851.238.177.109.689

1234567...22

2

7

1.427

3.169

85.829

2.271.991.367.799.686.681.549

Sm18 = p1 * (p1)^2 * p2 * p5 * p18

2 *

3^2 *97 *

88241 *

801309546900123763

Sm19 = p2 * p2 * p2 * p3 * p4 * p18

13 *

43 *

79 *

281 *

1193 *

833929457045867563

Sm20 = (p1)^5 * p1 * p1 * p6 * p7 * p16

2^5 *

3 *

5 *

323339 *3347983 *

2375923237887317

Sm21 = p1 * p2 * p2 * p2 * p3 * p3 * p6 * p18

3 *

17 *37 *

43 *

103 *

131 *

140453 *

802851238177109689





1234567...23

341

769

13.052.194.181.136.110.820.214.375.991.629

1234567...24

22

3

7

978.770.977.394.515.241

1.501.601.205.715.706.321

1234567...25

52

15.461

31.309.647.077

1.020.138.683.879.280.489.689.401

1234567...26

2

34

21.347

2.345.807

982.658.598.563

154.870.313.069.150.249

1234567...27

33

192

4.547

68.891

40.434.918.154.163.992.944.412.000.742.833

Sm22 = p1 * p1 * p4 * p4 * p5 * p22

2 *

7 *

1427 *

3169 *

85829 *

2271991367799686681549

Sm23 = p1 * p2 * p3 * p32

3 *

41 *

769 *

13052194181136110820214375991629

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

2^2 *

3 *

7 *

978770977394515241 *

1501601205715706321

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

5^2 *15461 *

31309647077 *

1020138683879280489689401

Sm26 = p1 * (p1)^4 * p5 * p7 * p12 * p18

2 *

3^4 *

21347 *

2345807 *982658598563 *

154870313069150249

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

3^3 *





1234567...28

23

47

409

416.603.295.903.037

192.699.737.522.238.137.890.605.091

1234567...29

3

859

24.526.282.862.310.130.729

19.532.994.432.886.141.889.218.213

1234567...30

2

3

5

13

49.269.439

370.677.592.383.442.753

17.333.107.067.824.345.178.861

1234567...31

29

2.597.152.967

163.915.283.880.121.143.989.433.769.727.058.554.332.

117

1234567...32

22

3

7

45.068.391.478.912.519.182.079

326.109.637.274.901.966.196.516.045.637

19^2 *

4547 *

68891 *

40434918154163992944412000742833

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

2^3 *

47 *

409 *

416603295903037 *

192699737522238137890605091

Sm29 = p1 * p3 * p20 * p26

3 *859 *

24526282862310130729 *

19532994432886141889218213

Sm30 = p1 * p1 * p1 * p2 * p8 * p18 * p23

2 *

3 *

5 *13 *

49269439 *

370677592383442753 *

17333107067824345178861

Sm31 = p2 * p10 * p42

29 *

2597152967 *

163915283880121143989433769727058554332117

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

2^2 *

3 *

7 *

45068391478912519182079 *

326109637274901966196516045637

of 32All the prime factors of the Smarandache Concatenated Numbers upto the first not fact ...




1234567...33

3

23

269

7.547

116.620.853.190.351.161

7.557.237.004.029.029.700.530.634.132.859

1234567...34

2

6.172.839.455.055.606.570.758.085.909.601.061.116.

212.631.364.146.515.661.667

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

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

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

1234567...38

Sm33 = p1 * p2 * p3 * p4 * p18 * p31

3 *23 *

269 *

7547 *

116620853190351161 *

7557237004029029700530634132859


2 *

6172839455055606570758085909601061116212631364146515661667

Sm35 = (p1)^2 * p1 * p3 * p3 * p8 * p10 * p37

3^2 *

5 *

139 *

151 *

64279903 *

4462548227 *

4556722495899317991381926119681186927

Sm36 = (p1)^4 * (p1)^2 * p3 * p3 * p56

2^4 *

3^2 *

103 *

211 *

39448709943503776711542648338171477043440283875433388943

Sm37 = p2 * p5 * p7 * p52

71 *

12379 *

4616929 *

3042410911077206144807069396988766146557218727107817





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

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

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

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

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

Sm38 = p1 * p1 * p23 * p43

2 *

3 *

86893956354189878775643 *

2367958875411463048104007458352976869124861

Sm39 = p1 * p2 * p3 * p4 * p25 * p36

3 *

67 *

311 *

1039 *

6216157781332031799688469 *

305788363093026251381516836994235539

Sm40 = (p1)^2 * p1 * p4 * p5 * p6 * p10 * p20 * p26

2^2 *

5 *

3169 *

60757 *

579779 *4362289433 *

79501124416220680469 *

15944694111943672435829023

Sm41 = p1 * p3 * p6 * p8 * p56

3 *

487 *

493127 *

32002651 *53545135784961981058419604998638516483529257158438201753

Sm42 = p1 * p1 * p3 * p3 * p11 * p25 * p34





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

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

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

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

2 *

3 *

127 *

421 *

22555732187 *

4562371492227327125110177 *

3739644646350764691998599898592229

Sm43 = p1 * p2 * p3 * p72

7 *

17 *

449 *

231058353953907153927797941629430896528705484237484443924582239474910453

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

2^3 *

3^2 *

12797571009458074720816277 *

1339846151380678925030581935625950075102697197563351

Sm45 = (p1)^2 * p1 * p1 * p2 * p3 * p4 * p13 * p18 * p41

3^2 *

5 *

7 *

41 *

727 *

1291 *

2634831682519 *

379655178169650473 *

10181639342830457495311038751840866580037

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

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

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

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

Sm47 = p1 * p4 * p6 * p22 * p53

3 *4813 *

679751 *

4626659581180187993501 *

27186948196033729596487563460186407241534572026740723

Sm48 = (p1)^2 * p1 * p3 * p4 * p7 * p29 * p462^2 *

3 *

179 *

1493 *

1894439 *

15771940624188426710323588657 *

1288413105003100659990273192963354903752853409

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

23 *

109 *

3251653 *

2191196713 *

53481597817014258108937 *

12923219128084505550382930974691083231834648599

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

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

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

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

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

Sm51 = p1 * p20 * p73

3 *

17708093685609923339 *

2323923950500978408934946776574079545611397611995364705071565292612305003

Sm52 = (p1)^7 * p17 * p76

2^7 *

43090793230759613 *

2238311464092386636761884511894978048448617178182150344531477542781856216843

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

3^3 *

7^3 *

127534541853151177 *

1045271879581348729278017817925065799872257805888381045072615907010178634849

Sm54 = p1 * (p1)^6 * p2 * p3 * p4 * p5 * p11 * p22 * p51

2 *

3^6 *

79 *

389 *

3167 *

13309 *

69526661707 *

8786705495566261913717 *

107006417566370797549761092803112128112769421435739

Sm55 = p1 * p9 * p15 * p22 * p55

5 *

768643901 *





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

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

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

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

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

641559846437453 *

1187847380143694126117 *

4215236719202000513320239996510510828557825033460062191

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

2^2 *

3 *

4324751743617631024407823 *

23788800764365032854813369830458732886158417401021113465643479155975828316681

Sm57 = p1 * p2 * p8 * p13 * p37 * p47

3 *

17 *

36769067 *

2205251248721 *

2128126623795388466914401931224151279 *

14028351843196901173601082244449305344230057319

Sm58 = p1 * p2 * p31 * p75

2 *

13 *

1448595612076564044790098185437 *

327789067063631145720134335581588856152921479945230066396717484857630796759

Sm59 = p1 * p18 * p36 * p55

3 *

340038104073949513 *

324621819487091567830636828971096713 *

3728107520554143574058126525447653708074390492098041537

Sm60 = (p1)^3 * p1 * p1 * p2 * p3 * p104





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

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

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

1234567...64

22

7

17

19

197

522.673

1.072.389.445.090.071.30720.203.723.083.803.464.811.983.788.589

611.891.180.337.745.942.599.768.541.236.768.900.814.

521.123.060.392.220.304.537

2^3 *

3 *

5 *

97 *

157 *

67555753880267981819314968257940564232852139165917171861439543181780049107204700168947673874146559500327

Sm61 = p8 * p14 * p92

10386763 *

35280457769357 *

33689963756771087787406890988794422071942750389483226687410462898596940470571223420915460371

Sm62 = p1 * (p1)^2 * p4 * p6 * p7 * p34 * p64

2 *

3^2 *

1709 *

329167 *

1830733 *

9703956232921821226401223348541281 *

6862941251271421600892952202464376235224342144596167046191804311

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

3^2 *

17028095263 *

2435984189933032657913735712547671618367909 *

330698276590517405413770500371046766676563523569978590938716221

Sm64 = (p1)^2 * p1 * p2 * p2 * p3 * p6 * p19 * p29 * p60

2^2 *

7 *

17 *

19 *

197 *

522673 *

1072389445090071307 *

20203723083803464811983788589 *





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

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

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

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.

012.035.286.59749.798.299.077.316.075.944.525.952.275.152.868.666.

920.234.906.076.151.289

1234567...69

611891180337745942599768541236768900814521123060392220304537

Sm65 = p1 * p1 * p2 * p5 * p43 * p70

3 *

5 *

31 *

83719 *

8018741962917674781000851595476715337223177 *

3954865825608609239925917139441010044747553878722812487568124023324127

Sm66 = p1 * p1 * p1 * p5 * p6 * p36 * p36 * p39

2 *

3 *

7 *

20143 *

971077 *

319873117219722504963051951872747251 *

927600480728565729398211282118577179 *

506464674142683362314480915373647544917

Sm67 = p3 * p18 * p105

397 *

183783139772372071 *

169207186381096030569641287629182352063847752831832860300985727686482291228260812667458777140342739211041

Sm68 = (p1)^4 * p1 * p2 * p9 * p10 * p50 * p56

2^4 *

3 *

23 *

764558869 *

1811890921 *

16210201583355429120740178111425145802012035286597 *

49798299077316075944525952275152868666920234906076151289





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

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

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

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

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.

Sm69 = p1 * p2 * p2 * p22 * p24 * p32 * p49

3 *13 *

23 *

8684576204660284317187 *

281259608597535749175083 *

15490495288652004091050327089107 *

3637485176043309178386946614318767365372143115591

Sm70 = p1 * p1 * p7 * p24 * p41 * p60

2 *

5 *

2411111 *

109315518091391293936799 *

11555516101313335177332236222295571524323 *

405346669169620786437208619979711016226055320437594464205451

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

3^2 *

83 *

2281 *

7484379467407391660418419352839 *

96808455591058960266687738381050176698103277406505724847082994829643349780363432993640165860627

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

2^2 *

3^2 *

5119 *

596176870295201674946617769 *

1123704769960650101739921630151581054522510738566183226239911321871780637830758881774623162921434662407





341.395.186.600.971.262.233.773.863.756.955.874.

363.353.778.851

1234567...74

2

3

71.788.313

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

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

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

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)

Sm74 = p1 * p1 * p1 * p7 * p8 * p20 * p25 * p31 * p49

2 *

3 *

7 *

1788313 *

21565573 *

99014155049267797799 *

1634187291640507800518363 *

1981231397449722872290863561307 *2377534541508613492655260491688014802698908815817

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

3 *

5^2 *

193283 *38824496309870038690197243565592769246963314017 *

219358378032318168161320006998916878634145966511629131235131312083699783021949850982403

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





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


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

1234567...79

73

137

22.683.534.613.064.519.783

132.316.335.833.889.742.191.77335.488.612.864.124.533.038.957.177.977

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

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

2^3 *

828699354354766183 *

213643895352490047310058981 *

8716407028594814374740596028898426313034395366012872513707917231855753694435270081076237925828389

Sm77 = p1 * p24 * p24 * p39 * p58

3 *

383481022289718079599637 *

874911832937988998935021 *

164811751226239402858361187055939797929 *

7442132227048590901854639419294226672231934035068486536423

Sm78 = p1 * p1 * p2 * p6 * p57 * p83 ( Sean A. Irvine )

2 *

3 *

31 *

185897 *

205155431830422787082756234197593935249202704547671264423 *

17403902113720391120287411398887911225298966708915583006414519403038472992542973083

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

73 *

137 *

22683534613064519783 *

132316335833889742191773 *

35488612864124533038957177977 *

11589330059060921218833486882285427414280233987959540582909167514265308253

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

2^2 *

3^3 *

5 *

101 *





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

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


3

53

503177.918.442.980.303.859

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

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

10263751 *

1295331340195453366408489 *

1702600917839548328745392482587491026230318172323434581398602992701169952537157469971305061091390839579932352102383

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

3^3 *

509 *

152873624211113444108313548197 *

58762581888644185603361112342786137599799640821735382180404307223995625796855706598141292123658134092320545833186103

Sm82 = p1 * p2 * p4 * p5 * p35 * p42 * p70

2 *

29 *

4703 *

10091 *

12295349967251726424104854676730107 *

334523571229968373890203385137399026475051 *

1090461105551993653223776199179348475393504023636425991597284018461539


3 *

53 *

503 *

177918442980303859 *

21875480270521598141087357354188092945840550359281483 *

3966169790267211790412249283896602109358687165012835285295541472324348526743126307

by SNFS, 8 days

Sm84 = (p1)^5 * p1 * p157

2^5 *

3 *1286008219803251368907934564500221065877631534197190762847328503894160459817025473591130156786722443288099853756419412985069550726116382682






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


2

323

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


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


22

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

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.


3 *

7 *

231330259 *

4275444601 *

101784611215757903569658774280830604745279416597473 *

58398250025786270255235847423735930777973447337337804788906368149837276410666257137526766841721

Sm87 C145 = (p51) * (p95)

by SNFS, 14 days.





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


32

13

31

97

163.060.459

789.841.356.493.369.879496.118.159.817.126.721.484.175.235.476.073

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


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


37

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

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

3^2 *

13 *

31 *

97 *

163060459 *

789841356493369879 *

496118159817126721484175235476073 *

26459905787227421825352754831024262009257 *

2075552579046417801880667285191357553672027185826871770761977511

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





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

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

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

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


37 *

607 *5713601747802353 *

100397446615566314002487 *

3581874457050057021838729610409482762969149632972915379 *

267535593139950330755907265689770024664090795106497661308268157342396003221

Sm91 C129=

(p55) * (p75)

by GNFS, 4 days

Submitted on Monday October 24, 2005 22:51

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

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





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


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

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

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

1234567...98 (by Philippe Strohl)

2

32

23

37

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


3 *

5 *

7 *

401 *

244987542265129586458446183157595351 *

11968433332458576038029692527873667705299166706759846553511908664112230897725465255076396469755430229667799116144000

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

2^2 *

3 *

23 *

60331 *

7414218343605898007054904008539678229463872328651811494111562828507144051357405695052612835346584059319708614758837877621899193657692066488

Sm97 = p2 * p183

13 *

9496676084700933185781670630155478640327125175610024094872579721064569549418034266519115003963488811973660458508943357428205913054397902882





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

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

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

1234567...101

3

8.377

799.917.088.062.980.754.649

6.141.298.867.893.783.540.378.996.188.437.492.127.

764.003.798.590.081.909.642.744.192.552.148.805.

391.571.094.462.286.943.973.793.319.310.495.244.

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

2 *

3^2 *23 *

37 *

199 *

1495444452918817 *

381502754125464943168932369122248696781 *

3588472635471667861938967869443938442910813342994227048889 *

197825482406769698151783117995020967519766027202915861687264259155363

Sm99 = (p1)^2 * p5 * p12 * p65 * p107 ( 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

Sm100 = (p1)^2 * (p1)^2 * (p1)^3 * p4 * p7 * p10 * p20 * p30 * p118 ( Sean A. Irvine )

2^2 *

5^2 *

7^3 *

8171 *

1065829 *

2824782749 *

20317177407273276661 *

970447246795177523033247400823 *

74205783828993990282844643926514529377440398361853557786629614137808057343696437488052995898987761128049502342217845





779.697.771.718.230.720.369.645.297.842.348.701.

438.176.773.337.763.517.045.479 = c169

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

1234567...103

131

1.231

1.713.675.826.579.469

446.742.179.244.293.705.107.743.562.882.710.303.107.

653.012.176.267.248.963.278.610.465.019.097.212.

371.922.408.861.122.959.220.266.036.734.062.945.

987.327.999.759.759.889.653.172.480.328.343.669.

298.241.710.606.083.565.775.177.315.278.367 = c180

1234567...104

26

3

59

773

19.601.852.982.312.892.289

719.258.686.675.513.979.262.824.247.665.486.572.432.830.986.721.319.631.951.392.684.768.588.734.879.

818.050.477.878.475.895.676.175.151.494.878.249.

756.161.105.289.114.143.497.898.340.693.385.704.

920.480.426.209.979.668.623.253.319.269 = c177

Sm101 = p1 * p4 * p21 * c169

3 *

8377 *

799917088062980754649 *

6141298867893783540378996188437492127764003798590081909642744192552148805391571094462286943973793319310495244779697771718230720369645297842

Sm102 = p1 * p1 * p2 * p2 * p4 * p5 * p5 * p10 * p172

2 *3 *

19 *

89 *

3607 *

15887 *

32993 *

2865523753 *

2245981950884772863770930273540385579914865629636627917458256811732689892492870743326877749976350147897124023992523914020180640624011740696

Sm103 = p3 * p4 * p16 * c180

131 *

1231 *

1713675826579469 *

4467421792442937051077435628827103031076530121762672489632786104650190972123719224088611229592202660367340629459873279997597598896531724803

Sm104 = (p1)^6 * p1 * p2 * p3 * p20 * c177

2^6 *

3 *

59 *

773 *

19601852982312892289 *

7192586866755139792628242476654865724328309867213196319513926847685887348798180504778784758956761751514948782497561611052891141434978983406





1234567...105

3

5

193

6.942.508.281.251

6.142.568.425.081.438.832.759.347.097.237.645.657.

628.988.841.290.897.653.306.131.105.424.225.283.

715.083.312.222.699.695.626.373.378.408.508.801.

576.676.945.473.675.560.832.710.564.855.374.168.

538.899.701.991.629.924.122.849.992.620.409.192.891.550.349 = c190

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

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

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

Sm105 = p1 * p1 * p3 * p13 * c190

3 *

5 *

193 *

6942508281251 *

6142568425081438832759347097237645657628988841290897653306131105424225283715083312222699695626373378408508801576676945473675560832710564855

Sm106 = p1 * p2 * p3 * p3 * p29 * p35 * p69 * p71 ( 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

Sm107 = (p1)^3 * p12 * p199

3^3 *

536288185369 *

8526150295974562563911703097396807303361305853752080385827103422281006173895434732314352853475423512542010066856002013066381244223149688686





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

In the Queue

Sm116 (COMPLETE) by Sean A. Irvine

2^2

3^2

2239

9787002048140152171263515060558503699 (p37)

1564979683672455156550590564550896170739590132221492657705868045238053081655725205100502721369811982/50507087284878063256342705928229557508508670247743582143974583381133763456377474127925121483818271 (p198)

Sm117 (PARTIAL) by Philippe Strohl

3^2

31883

333699561211(p12 by MF)

28437086452217952631(p20 by MF)

4533906451347845613823069537391478156136844054596308469800656338667810383531584928935260534747032327/

7527359676572226592530190953518990632828989750268624468732498680573884588879299814792334945634701707/

955171 (c206)

Philippe Strohl found a new factor of Sm117 (but the cofactor is still composite) :

( Friday 22/08/2008 14:59 )

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 1567405msStep 2 took 365869ms

********** Factor found in step 2: 29899433706805424728763564400367447

Found probable prime factor of 35 digits: 29899433706805424728763564400367447

Composite cofactor

1516385392381488800257172455421115218103131389426237636403907504872104848630821256747576627427151045/

955402969807173970504574397911322632329216437824800943241454211577975893 has 172 digits


278240783 (p9)

105299178204417486675841093021769 (p33)

4213754301973277818574830150933029703205115128282586723382785882706969263182976786615125991432774212/

6655712800813928005415583544197992453104126217919256625510887081121101381586161564163756343745220847/

88731721938623 (p214)


2^2

197

1192717377

273131

623321

3417425341307 (p13)

4614988413949 (p13)

8817212782626223819399721069204897 (p34)

3193000701568524782467188898304641220775712837053116231323237434768208956576768718690200934704769644/

9776432217795787176033049303491281548912080640497966801122571925082634457098946350721137505551941519/

011986808243341521869976182605502561225915860092642869 (p254)


2^4

3^2

131

10613

29354379044409991753 (p20)

Sm108 = (p1)^2 * (p1)^3 * p18 * p36 * p161 ( Sean A. Irvine )

2^2 *

3^3 *

128451681010379681 *

132761751746390611923240080737166083 *

6703142557817928040555348648900674233695375904983084080935101634841300766484581974276898497657520542683339952501046261431761333328461563935





2587833772662908004979 (p22)

4103096315830350734534473515557 (p31)

12805089500421274253268517941967 (p32)

17815076027044127272632744936161 (p32)

8672648427724666836335878649605123533671234498113722493001839423884394310675246313883662523667972796/

2252207354099527091658621300178181661297993537192234834905032751669182605720711181867690701061985005/

06817 (p205)


3

5

7

1331

247007767 (p9)

490242053931613 (p15)

13183356310254866666237435750357 (p32)

1827567681941731356121062274519777291863760972834724140109364732283149431121763995026237820114303681/

5496592791501562871236022199555066011298451642231401735631929300761746199878863922607830081439132951/

8357914807533066417404260975659341568447505060701439696780455579283391217843114550193398184405873168/

7369979309788684753888188553 (p328)


2^4

7

59

191

1093

1223

22521973429 (p11)

15219125459582087 (p17)

158906425126963139 (p18)

2513521443592870099 (p19)

677008100402429325901609057 (p27)

7894977574571781556444786202593614139721506720817604366015528775760676373160442530345019483307700978/

5930092303778152032404551795675090170923053660293230843498614359663939844365627366165832785305317365/

4182408958317242742517820581180854453052925226658686768857580470091786086406610221754789129568203967/

384451608838167466879488313009807568569387 (p342)


349

506442073 (p9)

1080829169904060835770214147747 (p31)

6462532135259365632021314942658431728094733620599149141734327082367671298692320282350900597278296365/

5379540884023312710555856177308446767405172970938977772676796780228431702242816509113421339444592236/

2621714833233212554723714564174418111669498936207951085298551799080803363445759267522417246541605647/

9089775584237803310812087978174533031535543826808011950270774768093377786126458352214138913849333920/

84296657173 (p411)


3

5397

21728563

300856949 (p9)

554551531 (p9)

8174619091 (p10)

165897663095213559529993681 (p27)

4216891792160044902686705799521388925390732888122432608757782570720072408665875338945809590873483499/

4620499297336767795766591884079938389340512146288914907796490815205714454677249295016313996731519073/

1294500128685930803732434591580562083296784964092846142348549703545534554252170080984646226664593569/

3244989301840859149448482745301257117142121991254187915811979621816086743861383233522991211424294391/

495728519167 (p412)



all the prime factors of the smarandache concatenated numbers upto the first not factor

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