All the prime factors of the Reversed Smarandache Concatenated Numbers upto the first

8/9/2019 All the prime factors of the Reversed Smarandache Concatenated Numbers upto the first...

http://slidepdf.com/reader/full/all-the-prime-factors-of-the-reversed-smarandache-concatenated-numbers-upto 1/28



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

Messages

[ June 1, 2008 ]Greg Childers (email) factorized Rsm96 ! [ go to entry ]

Patrick,

I decided to run a little ECM on the 7 remaining Rsm's 100 and below, and found a factor.Rsm96 splits as p41 * p131.

P41: 82514915741623328517650484573901437176111P131:79276466536870215660589427037258187228232511168042181233242100341381290510746535680251722466853314074942409563489786970760805952371B1: 3000000Sigma: 2833338313

Greg

[ May 27, 2008 ]Greg Childers (email) factorized Rsm89 & Rsm92 ! [ go to entry ]

Hi Patrick,

Here are a couple more factorizations, both by SNFS using GGNFS and msieve.At this point, they are getting more difficult so more ECM is needed.

Rsm89P50: 49388406496643388078114888189038555500608342769177P111: 150924360170891168648756251949784084919713735816964351919278654382818389528776733970746808714702822077767563109

Rsm92P43: 5493464474242305396221143000161670754181497P84: 275430796569999455663492846893637583669272814955746117769050223296905117622304550539

Greg

[ November 24, 2007 ]Greg Childers (email) factorized Rsm88 ! [ go to entry ]

Hi Patrick,

Here are the factors of Rsm88. This was completed using SNFS.GGNFS was used for the sieving and msieve for the post-processing.

p65: 10667225358631834515761916285328371530256362233450556142314335489

p98: 13048607496185224796929295956451966027944274230342704636654403499300276689269285063289558739924219

Greg

[ August 28, 2005 ]Philippe Strohl (email) completely factorized Rsm80 to Rsm87! [ go to entry ]

Hi Patrick !

I have noticed a regain of interest for smarandacheconcatenated numbers...

I have done some ecm work on them a year ago...

Since Bob factorized Rsm78, I can send you the completefactorization of Rsm from 80 to 87... (results for Rsm 81, 82, 85and 87 are archived on M Fleuren pages). I also have found someother factors I'll list at the end of this post since theyaren't reported elsewere...

Thanks a lot for maintaining these pages.

Best regards.Philippe Strohl.

Reporting a PARTIAL factorization of Rsm92 3.17.113.376589.3269443.6872137

Page 2 of 28All the prime factors of the Reversed Smarandache Concatenated Numbers upto the first ...

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



c153:1905562152576517700991248912769311100544276292351653171684499539309179/ 8417258481820725908693449773331774186663993549906216716372511851965313/ 8300365290533

Line=28/35 Curves=30/1100 B1=1000000 factors=1C153 Using B1=1000000, B2=839549780, polynomial Dickson(6),sigma=4139260630Step 1 took 149312msStep 2 took 96974ms********** Factor found in step 2: 125940177196545564166916551Found probable prime factor of 27 digits:

125940177196545564166916551

P.S. : I have found some interesting "not so small" factors forsome composites up to 100 (like a p45 not reported yet) andcompleted some of the smarandache and reverse smarandachenumbers (but not the smallest).

To avoid duplication, would you mind to keep tracks of themhere since your pages have a new form or do you prefer continueto record only results for the smallest unfactored number,which nicely increase the suspens and emulation ?...

What I mean is that your pages could mention that these numbers arecompletely factored so that nobody will re-do ecm up to 40-45 digits orworst snfs these numbers...Even if you don't enter in details, I would suggest simply that the colourof the links of the top of the pages changes depending of the status of thenumber.For example : grey for factored (even for numbers greater than Sm83 and

Rsm88), violet for unfactored "please refer to M Fleuren text file" and whynot yellow for "an unreported factor is known, please contact me for details"...You would just have to add a legend below the links...

Philippe, your arguments are very convincing, so I will follow and implementyour suggestions, with pleasure. Thanks for helping to improve this site.Much obliged. Patrick.

[ August 27, 2005 ]Robert Backstrom (email) factorized Rsm78 ! [ go to entry ]

Hello Patrick,

Here are the factors of Rsm78:3 *17 *47 *17795025122047 (p14) *78119581556663469779307447735538451582384717692143654960846437 (p62) *236415864091491721631173832082837638453438349732083245678426495346687 (p69)

They were found with GGNFS (version: 0.77.1).

See summary file, below.

Cheers,--Bob.

[ June 28, 2005 ]Robert Backstrom (email) factorized Rsm76 ! [ go to entry ]

Hello Patrick,

Here are the factors of Rsm76 and Rsm77 for your tables.

Rsm76 was done using GGNFS (written by Chris Monico),and I'll include the summary file below.

Rsm77 was done using ECM.

[ December 30, 2003 ]Philippe Strohl (email) completely factorized Rsm67 ! [ go to entry ]

Hello Patrick !

I wrote to you a few months ago for the factorization of the Rsm65.I'm now back with the harder factorization of Rsm67, a c113 that is in fact





a p40 * p73... It tooks me more than 2300 curves with gmp-ecm 5.0at B1=3 000 000 to catch them (with a celeron 400)...

The next "unknown factorization" for reversed smarandache concatenatednumbers seems to be Rsm76...

To be continued !

[ July 24, 2003 ]Philippe Strohl (email) found all the factors of Rsm65 ! [ go to entry ]

Hello Patrick!

My name is Philippe Strohl, I am a french Vet and a modest contributorof A Kulsha, H Mishima and D Alpern (modified fermat numbers) projects.

I don't know if this result was known (your site and M. Fleuren file seemsto say it wasn't) but I have factored reversed concatenated smarandache number 65by P-1 method.The factorisation is :Rsm65 = 65646362.....4321 = p1 * p1 * p2 * p5 *p5 * p31 * p79 = 3 * 7 * 23 * 13219 * 24371 *8388659548971249567207085659037 * (proven prime)5029201255469786028962125207969872821464255213510243858630692908421051327966799 (proven prime)

You will find the details following in this mail (gmp-ecm 5.1 beta output screen,p-1 factorisation of the number and Rsm66 and Rsm67 from M. Fleuren tables).I'm surprised that this "small" p31 hasn't been found before...

Philippe Strohl.

The List of Rsm Factors

1

1

21

3

7

321

3

107

4321

29

149

54321

3

19

953

Rsm1 = p1 = unity

1

Rsm2 = p1 * p1 = semiprime

3 *

7


3 *

107


29 *

149

Rsm5 = p1 * p2 * p3

3 *





654321

3

218.107

7654321

19

402.859

87654321

32

1.997

4.877

987654321

32

172

379.721

10987654321

7

28.84354.421

1110987654321

3

370.329.218.107

12...7654321 3

7

5.767.189.888.301

13...7654321

17

3.243.967

19 *

953


3 *

218107


19 *

402859

Rsm8 = (p1)^2 * p4 * p4

3^2 *1997 *

4877

Rsm9 = (p1)^2 * (p2)^2 * p6

3^2 *

17^2 *

379721

Rsm10 = p1 * p5 * p5

7 *

28843 *

54421


3 *

370329218107

Rsm12 = p1 * p1 * p13

3 *

7 *

5767189888301





237.927.839

14...7654321

3

11

24.769.1771.728.836.281

15...7654321

3

13

192

79

136.133.374.970.881

16...7654321

23

233

2.531

1.190.788.477.118.549

17...7654321

32

13

17.929

25.411

47.543

677.181.889

18...7654321

32

112

19

23

281

397

8.577.529

399.048.049

Rsm13 = p2 * p7 * p9

17 *

3243967 *

237927839

Rsm14 = p1 * p2 * p8 * p10

3 *

11 *

24769177 *

1728836281

Rsm15 = p1 * p2 * (p2)^2 * p2 * p15

3 *

13 *

19^2 *

79 *

136133374970881

Rsm16 = p2 * p3 * p4 * p16

23 *

233 *

2531 *

1190788477118549

Rsm17 = (p1)^2 * p2 * p5 * p5 * p5 * p9

3^2 *

13 *

17929 *

25411 *

47543 *

677181889

Rsm18 = (p1)^2 * (p2)^2 * p2 * p2 * p3 * p3 * p7 * p9





19...7654321

17

19

1.462.095.938.449

40.617.114.482.123

20...7654321

3

89

317

37.889

629.639.170.774.346.584.751

21...7654321

3

37

732.962.679.433

2.605.975.408.790.409.767

22...7654321

13

137

178.489

1.068.857.874.509

65.372.140.114.441

23...7654321

3

7

191

578.960.862.423.763.687.712.072.079.528.211

3^2 *

11^2 *

19 *

23 *

281 *

397 *

8577529 *

399048049

Rsm19 = p2 * p2 * p13 * p14

17 *

19 *

1462095938449 *

40617114482123

Rsm20 = p1 * p2 * p3 * p5 * p21

3 *

89 *

317 *

37889 *

629639170774346584751

Rsm21 = p1 * p2 * p12 * p19

3 *

37 *732962679433 *

2605975408790409767

Rsm22 = p2 * p3 * p6 * p13 * p14

13 *

137 *

178489 *

1068857874509 *

65372140114441

Rsm23 = p1 * p1 * p3 * p33

3 *

7 *

191 *

578960862423763687712072079528211





24...7654321

3

107

457

57.527

28.714.434.377.387.227.047.074.286.559

25...7654321

11

31

59

158.820.811

410.201.377

19.258.319.708.850.480.997

26...7654321

33

929

1.753

2.503

4.049

11.171

527.360.168.663.641.090.261.567

27...7654321

35

83

3.216.341.629

7.350.476.679.347

571.747.168.838.911.343

28...7654321

23

193

3.061

2.150.553.615.963.932.561

967.536.566.438.740.710.859

Rsm24 = p1 * p3 * p3 * p5 * p29

3 *

107 *

457 *57527 *

28714434377387227047074286559

Rsm25 = p2 * p2 * p2 * p9 * p9 * p20

11 *

31 *

59 *

158820811 *

410201377 *19258319708850480997

Rsm26 = (p1)^3 * p3 * p4 * p4 * p4 * p5 * p24

3^3 *

929 *

1753 *

2503 *4049 *

11171 *

527360168663641090261567

Rsm27 = (p1)^5 * p2 * p10 * p13 * p18

3^5 *

83 *

3216341629 *

7350476679347 *

571747168838911343

Rsm28 = p2 * p3 * p4 * p19 * p21

23 *

193 *

3061 *





29...7654321

3

11

709

105.971

2.901.761

1.004.030.749

405.373.772.791.370.720.522.747

30...7654321

3

73

79

18.041

24.019

32.749

5.882.899.163

209.731.482.181.889.469.325.577

31...7654321

7

30.331.061

147.434.568.678.270.777.660.714.676.905.519.165.947.

320.523

32...7654321

3

17

1.231

28.409

103.168.496.413

17.560.884.933.793.586.444.909.640.307.424.273

33...7654321

3

7

7.349

9.087.576.403

237.602.044.832.357.211.422.193.379.947.758.321.446.

2150553615963932561 *

967536566438740710859

Rsm29 = p1 * p2 * p3 * p6 * p7 * p10 * p24

3 *

11 *

709 *

105971 *

2901761 *

1004030749 *

405373772791370720522747

Rsm30 = p1 * p2 * p2 * p5 * p5 * p5 * p10 * p24

3 *

73 *

79 *

18041 *

24019 *

32749 *

5882899163 *

209731482181889469325577

Rsm31 = p1 * p8 * p45

7 *

30331061 *

147434568678270777660714676905519165947320523

Rsm32 = p1 * p2 * p4 * p5 * p12 * p35

3 *

17 *

1231 *

28409 *

103168496413 *

17560884933793586444909640307424273







38...7654321

3

9.833

130.084.529.452.972.348.314.460.579.180.389.918.709.

759.033.057.100.685.484.626.179

39...7654321

3

19

73

709

66.877

1.996.163.827.266.702.824.413.525.236.841.223.322.

799.723.697.285.999.656.577

40...7654321

11

41

199

537.093.776.870.934.671.843.838.337

837.983.319.570.695.890.931.247.363.677.891.299.117

41...7654321

3

29

41

89

3.506.939

18.697.991.901.857

59.610.008.384.758.528.597

3.336.615.596.121.104.783.654.504.257

42...7654321

3

13.249

14.159

25.073

6.372.186.599

4.717.130.738.223.261.316.867.440.830.358.870.217.

018.600.625.280.851

12729390074866695790994160335919964253

Rsm38 = p1 * p4 * p63

3 *

9833 *

130084529452972348314460579180389918709759033057100685484626179

Rsm39 = p1 * p2 * p2 * p3 * p5 * p58

3 *

19 *

73 *

709 *66877 *

1996163827266702824413525236841223322799723697285999656577

Rsm40 = p2 * p2 * p3 * p27 * p39

11 *

41 *

199 *

537093776870934671843838337 *

837983319570695890931247363677891299117

Rsm41 = p1 * p2 * p2 * p2 * p7 * p14 * p20 * p28

3 *

29 *

41 *

89 *

3506939 *18697991901857 *

59610008384758528597 *

3336615596121104783654504257

Page 11 of 28All the prime factors of the Reversed Smarandache Concatenated Numbers upto the fir ...




43...7654321

52.433

73.638.227.044.684.393.71711.246.650.506.151.248.047.514.771.323.412.217.987.

665.845.460.131.261

44...7654321

32

7

3.067

114.883

245.653

65.711.907.088.437.660.760.939

12.400.566.709.419.342.558.189.822.382.901.899.879.241

45...7654321

32

23

167

15.859

25.578.74332.406.938.830.550.964.081.541.672.531.706.672.083.

265.765.131.138.228.893.759.713.957

46...7654321

23

35.801

543.124.946.137

45.223.810.713.458.070.167.393

2.296.875.006.922.250.004.364.885.782.761.014.060.

363.847

47...7654321

3

11

Rsm42 = p1 * p5 * p5 * p5 * p10 * p52

3 *

13249 *

14159 *

25073 *

6372186599 *

4717130738223261316867440830358870217018600625280851

Rsm43 = p5 * p20 * p53

52433 *

73638227044684393717 *

11246650506151248047514771323412217987665845460131261

Rsm44 = (p1)^2 * p1 * p4 * p6 * p6 * p23 * p41

3^2 *

7 *

3067 *

114883 *

245653 *

65711907088437660760939 *

12400566709419342558189822382901899879241

Rsm45 = (p1)^2 * p2 * p3 * p5 * p8 * p65

3^2 *

23 *

167 *

15859 *

25578743 *

32406938830550964081541672531706672083265765131138228893759713957

Rsm46 = p2 * p5 * p12 * p23 * p43

23 *

35801 *

543124946137 *

45223810713458070167393 *

2296875006922250004364885782761014060363847





31

59

1.102.254.985.918.193

4.808.421.217.563.961.987.019.820.401

14.837.375.734.178.761.287.247.720.129.329.493.021

48...7654321

3

151

457

990.013

246.201.595.862.687

636.339.569.791.857.481.119.613

15.096.613.901.856.713.607.801.144.951.616.772.467

49...7654321

71

9.777.943.361

71.279.637.669.169.187.180.216.178.143.931.072.216.

235.463.059.085.052.636.143.589.860.866.110.201.

991

50...7654321

3

157

3.307

3.267.926.640.703

771.765.128.032.466.758.284.258.631.297

1.285.388.803.256.371.775.298.530.192.200.584.446.

319.323

51...7654321

3

11

15.607.560.143.831.952.831.034.557.389.011.016.191.

916.100.088.735.534.098.252.188.243.005.506.550.

042.821.851.848.110.737

Rsm47 = p1 * p2 * p2 * p2 * p16 * p28 * p38

3 *

11 *

31 *

59 *1102254985918193 *

4808421217563961987019820401 *

14837375734178761287247720129329493021

Rsm48 = p1 * p3 * p3 * p6 * p15 * p24 * p38

3 *

151 *

457 *990013 *

246201595862687 *

636339569791857481119613 *

15096613901856713607801144951616772467

Rsm49 = p2 * p10 * p77

71 *

9777943361 *

71279637669169187180216178143931072216235463059085052636143589860866110201991

Rsm50 = p1 * p3 * p4 * p13 * p30 * p43

3 *

157 *

3307 *

3267926640703 *

771765128032466758284258631297 *

1285388803256371775298530192200584446319323

Rsm51 = p1 * p2 * p92

3 *

11 *

15607560143831952831034557389011016191916100088735534098252188243005506550042821851848110737





52...7654321

7

29

670.001

403.520.574.901

70.216.544.961.751

1.033.003.489.172.581

13.191.839.603.253.798.296.021.585.972.083.396.625.

125.257.997

53...7654321

34

499

673

6.287

57.653

199.236.731

1.200.017.544.380.0231.101.541.941.540.576.883.505.692.003

2.061.265.130.010.645.250.941.617.446.327

54...7654321

33

74

13

1.427

632.778.317

57.307.460.723

7.103.977.527.461

617.151.073.326.209

2.852.320.009.960.390.860.973.654.975.784.742.937.

560.247

55...7654321

357.274.517

460.033.621

337.952.850.450.733.861.795.390.882.190.470.745.732.

440.551.509.303.900.198.252.202.379.628.657.263.

082.856.953

Rsm52 = p1 * p2 * p6 * p12 * p14 * p16 * p47

7 *

29 *

670001 *

403520574901 *

70216544961751 *

1033003489172581 *

13191839603253798296021585972083396625125257997

Rsm53 = (p1)^4 * p3 * p3 * p4 * p5 * p9 * p16 * p28 * p31

3^4 *

499 *

673 *

6287 *

57653 *

199236731 *

1200017544380023 *

1101541941540576883505692003 *

2061265130010645250941617446327

Rsm54 = (p1)^3 * (p1)^4 * p2 * p4 * p9 * p11 * p13 * p15 * p43

3^3 *

7^4 *

13 *

1427 *

632778317 *

57307460723 *7103977527461 *

617151073326209 *

2852320009960390860973654975784742937560247

Rsm55 = p9 * p9 * p84





56...7654321

3

132

85.221.254.605.693

130.893.658.529.726.305.450.095.097.258.014.177.208.

962.504.037.645.212.881.820.251.999.576.244.730.

152.822.433.471

57...7654321

3

41

25.251.380.689

185.341.405.391.688.249.727.709.433.589.302.205.214.

498.999.971.321.371.212.688.202.452.892.497.774.

826.168.815.604.386.643

58...7654321

11

2.425.477

178.510.299.010.259

377.938.364.291.219.561

5.465.728.965.823.437.480.371.566.249

5.953.809.889.369.952.598.561.290.100.301.076.499.

293

59...7654321

3

8.878.987.335.542.530.798.199.706.004.667

223.695.767.334.983.176.713.475.674.533.908.530.446.

231.765.827.709.335.846.079.166.299.801.865.160.

321

60...7654321

3

8.522.287.597

23.700.935.879.737.805.587.656.602.711.356.665.465.

672.635.558.102.860.173.996.672.149.163.434.889.

038.991.753.831.159.994.173.925.831

357274517 *

460033621 *

337952850450733861795390882190470745732440551509303900198252202379628657263082856953

Rsm56 = p1 * (p2)^2 * p14 * p87

3 *

13^2 *

85221254605693 *

130893658529726305450095097258014177208962504037645212881820251999576244730152822433471

Rsm57 = p1 * p2 * p11 * p933 *

41 *

25251380689 *

185341405391688249727709433589302205214498999971321371212688202452892497774826168815604386643

Rsm58 = p2 * p7 * p15 * p18 * p28 * p40

11 *2425477 *

178510299010259 *

377938364291219561 *

5465728965823437480371566249 *

5953809889369952598561290100301076499293

Rsm59 = p1 * p31 * p78

3 *

8878987335542530798199706004667 *

223695767334983176713475674533908530446231765827709335846079166299801865160321

Rsm60 = p1 * p10 * p101

3 *

8522287597 *

23700935879737805587656602711356665465672635558102860173996672149163434889038991753831159994173925831





61...7654321

13

373

6.399.032.721.246.153.065.183

214.955.646.066.967.157.613.788.969.151.925.052.620.

751

9.236.498.149.999.681.623.847.165.427.334.133.265.

556.780.913

62...7654321

32

11

487

6.870.011

3.921.939.670.009

11.729.917.979.119

9.383.645.385.096.969.812.494.171.823

43.792.191.037.915.584.824.808.714.186.111.429.193.

335.785.529.359

63...7654321

32

97

26.347

338.856.918.508.353.449.187.667

81.634.539.084.915.174.560.475.674.776.787.544.426.426.157.020.315.628.260.064.812.816.949.080.776.

530.011.946.073

64...7654321

397

653

459.162.927.787

27.937.903.937.681

386.877.715.040.952.336.040.363

50.238.676.722.181.090.702.078.407.150.521.845.843.

639.197.722.581.325.849.647.297.921

65...7654321 (by Philippe Strohl)

3

Rsm61 = p2 * p3 * p22 * p42 * p4613 *

373 *

6399032721246153065183 *

214955646066967157613788969151925052620751 *

9236498149999681623847165427334133265556780913

Rsm62 = (p1)^2 * p2 * p3 * p7 * p13 * p14 * p28 * p50

3^2 *

11 *

487 *

6870011 *

3921939670009 *

11729917979119 *

9383645385096969812494171823 *

43792191037915584824808714186111429193335785529359

Rsm63 = (p1)^2 * p2 * p5 * p24 * p86

3^2 *

97 *

26347 *

338856918508353449187667 *

81634539084915174560475674776787544426426157020315628260064812816949080776530011946073

Rsm64 = p3 * p3 * p12 * p14 * p24 * p65

397 *

653 *

459162927787 *

27937903937681 *

386877715040952336040363 *

50238676722181090702078407150521845843639197722581325849647297921





7

23

13.219

24.371

8.388.659.548.971.249.567.207.085.659.037

5.029.201.255.469.786.028.962.125.207.969.872.821.

464.255.213.510.243.858.630.692.908.421.051.327.

966.799

66...7654321

3

53

83

2.857

1.154.129

9.123.787

1.678.909.630.451.355.851.720.548.638.776.904.129.

368.032.732.116.932.059.545.601.625.238.248.196.

366.270.162.621.578.014.348.386.071.863


43

38.505.359.279

7.606.472.255.743.608.789.748.570.171.445.062.146.

361

5.372.806.591.299.678.424.830.025.693.429.256.401.

192.403.606.193.757.008.156.071.273.188.166.213

Rsm65 = p1 * p1 * p2 * p5 *p5 * p31 * p79 ( Philippe Strohl )

3 *7 *

23 *

13219 *

24371 *

8388659548971249567207085659037 *

5029201255469786028962125207969872821464255213510243858630692908421051327966799

Results for Rsm65(c110)

GMP-ECM 5.1-beta [powered by GMP 4.1] [P-1]

Input number is

42188257135394817340142497674838741348611344632218263720684041100069743522375803515655716220462441600170312563 (110

digits)

Using B1=500000000, B2=193112447595, polynomial x^60, x0=1652671375 Step 1 took 10590614ms (celeron 400 !) Step 2

took 4604770ms

********** Factor found in step 2: 8388659548971249567207085659037 Found probable prime factor of 31 digits:

8388659548971249567207085659037 Probable prime cofactor

5029201255469786028962125207969872821464255213510243858630692908421051327966799 has 79 digits

8388659548971249567207085659036=P1 * P1 * P1 * P2 * P2 * P3 * P4 * P6 * P6 * P11

P1 = 2 P1 = 2 P1 = 3 P2 = 11 P2 = 11 P3 = 769 P4 = 5981 P6 = 122701 P6 = 955697 P11 = 10711677421 cputime

0:00:00:34

Rsm66 = p1 * p2 * p2 * p4 * p7 * p7 * p103

3 *

53 *

83 *

2857 *

1154129 *

9123787 *

1678909630451355851720548638776904129368032732116932059545601625238248196366270162621578014348386071863

Rsm67 = p2 * p11 * p40 * p73 ( Philippe Strohl )

43 *

38505359279 *

7606472255743608789748570171445062146361 *

5372806591299678424830025693429256401192403606193757008156071273188166213

Results for Rsm67(c113)

GMP-ECM 5.1-beta [powered by GMP 4.1] [ECM]

Input number is 4086810427219739453580118808877441778190736752452460711071178179

7319877987395089517126726217960251669183401100893 (113 digits)

Using B1=3000000, B2=4016636514, polynomial Dickson(12), sigma=434847700

Step 1 took 351120ms


********** Factor found in step 2: 7606472255743608789748570171445062146361

Found probable prime factor of 40 digits: 7606472255743608789748570171445062146361





68...7654321

3

29

277.213

68.019.179

152.806.439

295.650.514.394.629.363

14.246.700.953.701.310.411

6.504.446.830.680.818.400.791.682.931.901.597.157.

630.284.650.677.644.922.374.842.962.527

69...7654321

3

11

71

1671.481

2.326.583.863

19.962.002.424.322.006.111.361

25.893.078.065.197.846.051.718.991.595.178.434.426.

254.383.595.503.019.580.054.933.145.462.167.064.

671.076.549.357.327

70...7654321

1.157.237

41.847.137

8.904.924.382.857.569.546.497

163.938.846.357.211.792.847.104.088.800.127.399.738.

668.867.423.240.262.451.107.510.450.122.250.847.

315.487.025.414.093.609.197

Probable prime cofactor 5372806591299678424830025693429256401192403606193757008156071273188166213 has 73 digits

factors proven primes by apr-cl : S. Tomabechi P-1

Jacobi Sum Test ( APR-CL )

for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71

for P=3 Q=7 13 31 61 19 37 181 43

for P=5 Q=11 31 61 181 71

for P=7 Q=29 43 71

final test

7606472255743608789748570171445062146361 is prime

cputime 0:00:01:33

Input a number ( Input 0 to exit )

Jacobi Sum Test ( APR-CL )for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 127 211 421 631 41 73 281

for P=3 Q=7 13 31 61 19 37 181 43 127 211 421 631 73

for P=5 Q=11 31 61 181 71 211 421 631 41 281

for P=7 Q=29 43 71 127 211 421 631 281

final test

5372806591299678424830025693429256401192403606193757008156071273188166213 is prime

cputime 0:00:04:17

Rsm68 = p1 * p2 * p6 * p8 * p9 * p18 * p20 * p67

3 *

29 *

277213 *

68019179 *

152806439 *

295650514394629363 *

14246700953701310411 *

6504446830680818400791682931901597157630284650677644922374842962527

Rsm69 = p1 * p2 * p2 * p3 * p4 * p10 * p23 * p89

3 *

11 *

71 *

167 *

1481 *

2326583863 *

19962002424322006111361 *

25893078065197846051718991595178434426254383595503019580054933145462167064671076549357327

Rsm70 = p7 * p8 * p22 * p96

1157237 *

41847137 *

8904924382857569546497 *

163938846357211792847104088800127399738668867423240262451107510450122250847315487025414093609197





71...7654321

32

17

131

16.871

1.504.047.269

82.122.861.127

1.187.275.015.543.580.261

144.604.206.245.872.959.501.627.508.393.777.181.764.

477.823.520.160.883.196.217.868.977.782.582.373.557.713.248.699

72...7654321

32

449

1.279

140.694.452.786.937.519.168.991.180.114.261.899.104.

420.602.632.532.713.737.057.441.161.711.270.533.

237.275.941.788.793.148.690.589.619.459.960.576.

436.357.556.531.306.839

73...7654321

7

11

21.352.291

1.051.174.71792.584.510.595.404.843

33.601.392.386.546.341.921

13.712.664.395.603.610.315.522.432.764.639.471.643.

768.450.652.229.502.858.089.980.699.747.050.646.

322.820.953

74...7654321

3177.337

6.647.068.667

31.386.093.419

669.035.576.309.897

4.313.244.765.554.839

67.415.094.145.569.534.144.512.937.880.453

346.129.598.050.812.738.223.913.038.086.154.784.537.

962.590.242.993

Rsm71 = (p1)^2 * p2 * p3 * p5 * p10 * p11 * p19 * p87

3^2 *

17 *

131 *

16871 *

1504047269 *

82122861127 *

1187275015543580261 *

144604206245872959501627508393777181764477823520160883196217868977782582373557713248699

Rsm72 = (p1)^2 * p3 * p4 * p129

3^2 *

449 *

1279 *

14069445278693751916899118011426189910442060263253271373705744116171127053323727594178879314869058961945996057643635

Rsm73 = p1 * p2 * p8 * p10 * p17 * p20 * p83

7 *

11 *

21352291 *

1051174717 *

92584510595404843 *

33601392386546341921 *

13712664395603610315522432764639471643768450652229502858089980699747050646322820953

Rsm74 = p1 * p6 * p10 * p11 * p15 * p16 * p32 * p51

3 *

177337 *





75...7654321

3

7

230.849

7.341.571

24.260.351

1.618.133.873

19.753.258.488.427

46.752.975.870.227.777

7.784.620.088.430.169.828.319.398.031

75.410.934.119.527.447.300.390.571.688.926.480.400.

272.241.123.206.797

76...7654321 (by Robert Backstrom )

53

975.061.812.023.238.350.627.523.821.635.806.428.720.

617.169.017.957.638.102.007.981

1.485.294.781.735.186.895.094.382.953.002.385.622.

013.684.184.993.264.316.509.378.497.928.610.042.

768.097

6647068667 *

31386093419 *

669035576309897 *

4313244765554839 *

67415094145569534144512937880453 *

346129598050812738223913038086154784537962590242993

Rsm75 = p1 * p1 * p6 * p7 * p8 * p10 * p14 * p17 * p28 * p53

3 *

7 *

230849 *

7341571 *

24260351 *

1618133873 *

19753258488427 *46752975870227777 *

7784620088430169828319398031 *

75410934119527447300390571688926480400272241123206797

Rsm76 = p2 * p63 * p79 ( Robert Backstrom )

53 *

975061812023238350627523821635806428720617169017957638102007981 *

1485294781735186895094382953002385622013684184993264316509378497928610042768097

Summary file for Rsm76(c142)

Number: Rsm_76

N=1448254221267371639012576691250218980350484066893443680178

957480272517436611204478557251570401942042879721553249283380

787097196473983226182157

( 142 digits)

SNFS difficulty: 146 digits.

Divisors found:

r1=97506181202323835062752382163580642872061716901795763810

2007981 (pp63)

r2=14852947817351868950943829530023856220136841849932643165

09378497928610042768097 (pp79)

Version: GGNFS-0.77.1

Total time: 248.93 hours.

Scaled time: 341.29 units (timescale=1.371).

Factorization parameters were as follows:

name: Rsm_76

n:144825422126737163901257669125021898035048406689344368017895

748027251743661120447855725157040194204287972155324928338078

7097196473983226182157

skew: 8.0

deg: 5

c5: 7523000

c0: 8790000000121

m: 10000000000000000000000000000

type: snfs

rlim: 6000000

alim: 6000000

lpbr: 29

lpba: 29

mfbr: 50

mfba: 50







79...7654321

160.591

274.591.434.968.167

1.050.894.390.053.076.193

1.721.746.072.956.576.690.202.206.138.718.569.810.

869.766.278.855.728.135.524.979.427.336.961.475.

483.160.058.092.704.761.582.299.124.638.700.313.

801


33

11

443.291

1.575.307

19.851.071.220.406.859

227.182.825.989.747.901.893.470.694.975.559

8.638.333.016.515.293.436.197.381.449.431.495.945.

464.563.125.030.491.266.044.550.972.970.223.270.

768.917.110.223.269

274925368143110340183242396198894897040039760682794559283704219

skew: 50.0

type: snfs

deg: 5

c5: 772100

c0: 8790000000121

m: 100000000000000000000000000000

rlim: 5500000

alim: 5500000

lpbr: 29lpba: 29

mfbr: 50

mfba: 50

rlambda: 2.5

alambda: 2.5

qintsize: 200000

Factor base limits: 5500000/5500000

Large primes per side: 3

Large prime bits: 29/29

Sieved special-q in [1100000, 9300001)

Relations: rels:15311202, finalFF:876116

Initial matrix: 761070 x 876116 with sparse part having weight 112078932.

Pruned matrix : 733239 x 737108 with weight 84286950.

Total sieving time: 206.74 hours.

Total relation processing time: 1.26 hours.

Matrix solve time: 20.61 hours.

Time per square root: 0.58 hours.

Prototype def-par.txt line would be:

snfs,150,5,0,0,0,0,0,0,0,0,5500000,5500000,29,29,50,50,2.5,2.5,100000total time: 229.19 hours.

--------- CPU info (if available) ----------

Athlon 64, 3200+ running Cygwin.

Rsm79 = p6 * p15 * p19 * p112

160591 *

274591434968167 *

1050894390053076193 *

1721746072956576690202206138718569810869766278855728135524979427336961475483160058092704761582299124638700313801

Rsm80 = (p1)^3 * p2 * p6 * p7 * p17 * p33 * p88 ( Philippe Strohl )

3^3 *

11 *

443291 *

1575307 *

19851071220406859 *

227182825989747901893470694975559 *

8638333016515293436197381449431495945464563125030491266044550972970223270768917110223269

RESULTS (all the probable primes have been verified primes by apr-cl)

Line=19/32 Curves=72/1000 B1=1000000 factors=1

C121 Using B1=1000000, B2=839549780, polynomial Dickson(6),

sigma=831649527





81...7654321

33

232

62.273

22.193

352.409

914.359.181.934.271

128.616.475.245.109.794.691.881.271.516.023.399.420.

747.375.754.647.255.684.774.783.381.708.606.008.

286.190.288.296.622.667.517.228.900.357.838.852.

877.964.197

82...7654321

82.818.079.787.776.757.473.727.170.696.867.666.564.

636.261.605.958.575.655.545.352.515.049.484.746.

454.443.424.140.393.837.363.534.333.231.302.928.

272.625.242.322.212.019.181.716.151.413.121.110.

987.654.321


3

1.974.871.757.105.304.370.241.687.597

1.414.913.491.576.959.991.085.772.193.821.333.363.

948.491.052.493.852.298.827.038.471.195.985.672.

820.912.298.157.918.486.848.781.698.715.932.375.

003.792.034.192.407.725.831

Step 1 took 16982ms

Step 2 took 13860ms

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

227182825989747901893470694975559

Found probable prime factor of 33 digits:

227182825989747901893470694975559

Probable prime cofactor

8638333016515293436197381449431495945464563125030491266044550972970223270768917110223269 has 88 digits

Rsm81 = (p1)^3 * (p2)^2 * p5 * p5 * p6 * p15 * p120

3^3 *23^2 *

62273 *

22193 *

352409 *

914359181934271 *

12861647524510979469188127151602339942074737575464725568477478338170860600828619028829662266751722890035783885287796

Rsm82 = PRIME!

828180797877767574737271706968676665646362616059585756555453525150494847464544434241403938373635343332313029282726252423222120191817161514

Rsm83 = p1 * p28 * p130 ( Philippe Strohl )

3 *

1974871757105304370241687597 *

14149134915769599910857721938213333639484910524938522988270384711959856728209122981579184868487816987159323750037920




sigma=3334714852


********** Factor found in step 1: 1974871757105304370241687597


1974871757105304370241687597






3

11

47

83447.841

18.360.053

53.294.058.577.163

9.982.711.074.569.412.202.184.829.872.323.289

125.041.734.265.706.422.786.569.078.989.578.766.735.

056.823.257.328.035.341.596.020.039.345.650.335.

832.474.986.014.272.849.361

85...7654321

465.619.934.881

5.013.354.844.603.778.080.337

36.776.645.009.790.287.118.723.906.169.819.493.438.

565.519.545.996.236.768.005.404.618.296.375.898.

835.476.299.088.296.154.006.135.887.578.611.770.

836.159.053.334.073.793


3

7

3.761

205.111

16.080.557

16.505.767

32.250.226.453.787.273.178.911.188.574.002.189

62.637.021.423.581.274.124.666.903.882.920.660.177.

315.636.462.243.958.664.624.625.942.830.414.280.

475.868.522.207.254.411.510.840.826.741


141491349157695999108577219382133336394849105249385229882703847

119598567282091229815791848684878169871593237500379203419240772

5831 has 130 digits

Rsm84 = p1 * p2 * p2 * p2 * p6 * p8 * p14 * p34 * p96 ( Philippe Strohl )

3 *

11 *

47 *

83 *

447841 *

18360053 *

53294058577163 *

9982711074569412202184829872323289 *125041734265706422786569078989578766735056823257328035341596020039345650335832474986014272849361




sigma=198298906


Step 2 took 83545ms


9982711074569412202184829872323289


9982711074569412202184829872323289


125041734265706422786569078989578766735056823257328035341596020

039345650335832474986014272849361 has 96 digits

Rsm85 = p12 * p22 * p128

465619934881 *

5013354844603778080337 *

36776645009790287118723906169819493438565519545996236768005404618296375898835476299088296154006135887578611770836159





87...7654321

3

2.423

4.433.139.632.126.658.657.934.801

951.802.198.132.419.645.688.492.825.211

28.648.431.477.796.086.247.464.902.964.197.486.005.

683.397.987.974.560.052.454.771.919.641.592.769.

777.638.753.833.612.094.955.143.339.736.919

88...7654321 (by Greg Childers)

73

8.747

10.667.225.358.631.834.515.761.916.285.328.371.530.

256.362.233.450.556.142.314.335.489

13.048.607.496.185.224.796.929.295.956.451.966.027.

944.274.230.342.704.636.654.403.499.300.276.689.

269.285.063.289.558.739.924.219


32

19

7.052.207

49.388.406.496.643.388.078.114.888.189.038.555.500.

608.342.769.177

150.924.360.170.891.168.648.756.251.949.784.084.919.

713.735.816.964.351.919.278.654.382.818.389.528.

Rsm86 = p1 * p1 * p4 * p6 * p8 * p8 * p35 * p104 ( Philippe Strohl )

3 *

7 *

3761 *

205111 *

16080557 *

16505767 *

32250226453787273178911188574002189 *

62637021423581274124666903882920660177315636462243958664624625942830414280475868522207254411510840826741




sigma=1952017108

Step 1 took 20761ms

Step 2 took 11392ms


32250226453787273178911188574002189


32250226453787273178911188574002189


626370214235812741246669038829206601773156364622439586646246259

42830414280475868522207254411510840826741 has 104 digits

Rsm87 = p1 * p4 * p25 * p30 * p107

3 *

2423 *

4433139632126658657934801 *

951802198132419645688492825211 *

28648431477796086247464902964197486005683397987974560052454771919641592769777638753833612094955143339736919

Rsm88 = p2 * p4 * p65 * p98 ( Greg Childers )

73 *

8747 *

10667225358631834515761916285328371530256362233450556142314335489 *

13048607496185224796929295956451966027944274230342704636654403499300276689269285063289558739924219

Summary for Rsm88(c162) = p65 * p98

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

and msieve for the post-processing.

Submitted on Sat, 24 Nov 2007 17:29:56 -0800





776.733.970.746.808.714.702.822.077.767.563.109


32

157

257

691

57.508.628.219.582.769.985.073

23.710.539.556.091.113.372.464.330.404.686.919

2.656.628.283.592.678.268.561.853.393.086.924.912.

569.196.381.871.916.529.968.854.546.224.536.796.

760.248.847.319.073.272.592.288.758.864.393


11

29

163

3.559

2.297

22.899.893

350.542.343.218.231

8.365.221.234.379.371.317.434.883

4.297.948.891.268.072.885.236.875.337.601

65.641.960.036.224.024.756.000.092.194.722.61711.412.914.421.079.678.469.007.301.289.508.708.061.

707.176.282.507


3

17

113

376.589

3.269.443

6.872.137

125.940.177.196.545.564.166.916.551

5.493.464.474.242.305.396.221.143.000.161.670.754.

181.497

275.430.796.569.999.455.663.492.846.893.637.583.669.

272.814.955.746.117.769.050.223.296.905.117.622.

304.550.539

Rsm89 = (p1)^2 * p2 * p7 * p50 * p111 ( Greg Childers )

3^2 *

19 *

7052207 *

49388406496643388078114888189038555500608342769177 *

150924360170891168648756251949784084919713735816964351919278654382818389528776733970746808714702822077767563109


Here are a couple more factorizations, both by SNFS using GGNFS and msieve (Rsm89 and Rsm92).Submitted on Tue, 27 May 2008 09:11 PM

Rsm90 = (p1)^2 * p3 * p3 * p3 * p23 * p35 * p106 ( Philippe Strohl )

3^2 *

157 *257 *

691 *

57508628219582769985073 *

23710539556091113372464330404686919 *

2656628283592678268561853393086924912569196381871916529968854546224536796760248847319073272592288758864393

Rsm91 = p2 * p2 * p3 * p4 * p4 * p8 * p15 * p25 * p31 * p35 * p50 ( Philippe Strohl )

11 *

29 *

163 *

3559 *

2297 *

22899893 *

350542343218231 *

8365221234379371317434883 *

4297948891268072885236875337601 *

65641960036224024756000092194722617 *

11412914421079678469007301289508708061707176282507






3

13

69.317

14.992.267

201.432.592.198.523.828.197.360.557.776.679.304.467.

257.143.112.125.068.672.607.007.837.316.638.653.

123

115.053.322.906.328.924.099.643.594.573.730.121.414.

771.889.862.698.591.137.393.328.485.987.955.147.

846.747.640.987

94...7654321

7

593

18.307

51.079.607.083

24.458.427.153.513.902.915.299.841.887.479.213.801.104.293.608.630.119.753.224.426.098.417.133.432.

885.515.941.461.781.399.350.023.357.950.489.971.

607.164.307.136.254.916.999.998.403.937.047.996.

183.765.840.955.991 = c161

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

In the Queue

Rsm95 (COMPLETE) by Greg Childers

Rsm92 = p1 * p2 * p3 * p6 * p7 * p7 * p27 * p43 * p84 ( Greg Childers )

3 *

17 *

113 *

376589 *

3269443 *

6872137 *

125940177196545564166916551 *

5493464474242305396221143000161670754181497 *

275430796569999455663492846893637583669272814955746117769050223296905117622304550539


Here are a couple more factorizations, both by SNFS using GGNFS and msieve (Rsm89 and Rsm92).

Submitted on Tue, 27 May 2008 09:11 PM

Rsm93 = p1 * p2 * p5 * p8 * p78 * p87 ( Greg Childers )3 *

13 *

69317 *

14992267 *

201432592198523828197360557776679304467257143112125068672607007837316638653123 *

115053322906328924099643594573730121414771889862698591137393328485987955147846747640987


This was completed by SNFS with Franke's lattice sieve and msieve.

Submitted on Sat, 5 Jul 2008 13:58 AM

Rsm94 = p1 * p3 * p5 * p11 * c161

7 *

593 *

18307 *

51079607083 *

2445842715351390291529984188747921380110429360863011975322442609841713343288551594146178139935002335795048997160716430713625491699999840393





And again...

Rsm95 = P46 * P121

P46: 1925519505985194246675568556102548265695431323

P121: 2238701414548422437837954711909075778087984958846007800228926253371628662089310781325800164276662804549907023877567116977

B1: 11000000

Sigma: 451237925

Greg

Submitted on Mon, 2 June 2008 06:50


I decided to run a little ECM on the 7 remaining Rsm's 100 and below, and found a factor.Rsm96 splits as P41 * P131.

P41: 82514915741623328517650484573901437176111

P131: 79276466536870215660589427037258187228232511168042181233242100341381290510746535680251722466853314074942409563489786970760805952371

B1: 3000000

Sigma: 2833338313

Submitted on Sun, 1 June 2008 22:49


ECM hit paydirt again...

Rsm100

P45: 600231117377832784458721416049204359605450473

P105: 933668601639537603239754327658420915210640646159004272796359399491722404669330495677171183756102624389829

B1: 11000000

Sigma: 3643562351

Greg

Submitted on Mon, 2 June 2008 04:30

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All the prime factors of the Reversed Smarandache Concatenated Numbers upto the first