Factorization websites

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

Messages

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

Hi Patrick !

I have noticed a regain of interest for smarandache
concatenated numbers...

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

Since Bob factorized Rsm78, I can send you the complete
factorization of Rsm from 80 to 87... (results for Rsm 81, 82, 85
and 87 are archived on M Fleuren pages). I also have found some
other factors I'll list at the end of this post since they
aren'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
c153:
1905562152576517700991248912769311100544276292351653171684499539309179/
8417258481820725908693449773331774186663993549906216716372511851965313/
8300365290533

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

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

To avoid duplication, would you mind to keep tracks of them
here since your pages have a new form or do you prefer continue
to 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 are
completely factored so that nobody will re-do ecm up to 40-45 digits or
worst snfs these numbers...
Even if you don't enter in details, I would suggest simply that the colour
of the links of the top of the pages changes depending of the status of the
number.
For example : grey for factored (even for numbers greater than Sm83 and
Rsm88), violet for unfactored "please refer to M Fleuren text file" and why
not 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 implement
your suggestions, with pleasure. Thanks for helping to improve this site.
Much obliged. Patrick.

[ August 27, 2005 ]
Robert Backstrom (email) factorized Rsm78 ! [ goto 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 ! [ goto 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 ! [ goto 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 5.0
at B1=3 000 000 to catch them (with a celeron 400)...

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

To be continued !

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

Hello Patrick!

My name is Philippe Strohl, I am a french Vet and a modest contributor
of 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 seems
to say it wasn't) but I have factored reversed concatenated smarandache number 65
by 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

Rsm1 = p1 = unity

1

 21
3
7

Rsm2 = p1 * p1 = semiprime
3 * 
7

 321
3
107

Rsm3 = p1 * p3 = semiprime
3 * 
107

 4321
29
149

Rsm4 = p2 * p3 = semiprime
29 * 
149

 54321
3
19
953

Rsm5 = p1 * p2 * p3
3 * 
19 * 
953

 654321
3
218.107

Rsm6 = p1 * p6 = semiprime
3 * 

218107

 7654321
19
402.859

Rsm7 = p2 * p6 = semiprime
19 * 

402859

 87654321
32
1.997
4.877

Rsm8 = (p1)^2 * p4 * p4
3^2 * 
1997 * 

4877

 987654321
32
172
379.721

Rsm9 = (p1)^2 * (p2)^2 * p6
3^2 * 
17^2 * 

379721

 10987654321
7
28.843
54.421

Rsm10 = p1 * p5 * p5
7 * 

28843 * 

54421

 1110987654321
3
370.329.218.107

Rsm11 = p1 * p12 = semiprime
3 * 

370329218107

 12...7654321
3
7
5.767.189.888.301

Rsm12 = p1 * p1 * p13
3 * 
7 * 

5767189888301

 13...7654321
17
3.243.967
237.927.839

Rsm13 = p2 * p7 * p9
17 * 
3243967 * 

237927839

 14...7654321
3
11
24.769.177
1.728.836.281

Rsm14 = p1 * p2 * p8 * p10
3 * 
11 * 
24769177 * 

1728836281

 15...7654321
3
13
192
79
136.133.374.970.881

Rsm15 = p1 * p2 * (p2)^2 * p2 * p15
3 * 
13 * 
19^2 * 
79 * 

136133374970881

 16...7654321
23
233
2.531
1.190.788.477.118.549

Rsm16 = p2 * p3 * p4 * p16
23 * 
233 * 
2531 * 

1190788477118549

 17...7654321
32
13
17.929
25.411
47.543
677.181.889

Rsm17 = (p1)^2 * p2 * p5 * p5 * p5 * p9
3^2 * 
13 * 
17929 * 
25411 * 
47543 * 

677181889

 18...7654321
32
112
19
23
281
397
8.577.529
399.048.049

Rsm18 = (p1)^2 * (p2)^2 * p2 * p2 * p3 * p3 * p7 * p9
3^2 * 
11^2 * 
19 * 
23 * 
281 * 
397 * 

8577529 * 

399048049

 19...7654321
17
19
1.462.095.938.449
40.617.114.482.123

Rsm19 = p2 * p2 * p13 * p14
17 * 
19 * 

1462095938449 * 

40617114482123

 20...7654321
3
89
317
37.889
629.639.170.774.346.584.751

Rsm20 = p1 * p2 * p3 * p5 * p21
3 * 
89 * 
317 * 

37889 * 

629639170774346584751

 21...7654321
3
37
732.962.679.433
2.605.975.408.790.409.767

Rsm21 = p1 * p2 * p12 * p19
3 * 
37 * 

732962679433 * 

2605975408790409767

 22...7654321
13
137
178.489
1.068.857.874.509
65.372.140.114.441

Rsm22 = p2 * p3 * p6 * p13 * p14
13 * 
137 * 
178489 * 

1068857874509 * 

65372140114441

 23...7654321
3
7
191
578.960.862.423.763.687.712.072.079.528.211

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

Rsm24 = p1 * p3 * p3 * p5 * p29
3 * 
107 * 
457 * 
57527 * 

28714434377387227047074286559

 25...7654321
11
31
59
158.820.811
410.201.377
19.258.319.708.850.480.997

Rsm25 = p2 * p2 * p2 * p9 * p9 * p20
11 * 
31 * 
59 * 

158820811 * 

410201377 * 

19258319708850480997

 26...7654321
33
929
1.753
2.503
4.049
11.171
527.360.168.663.641.090.261.567

Rsm26 = (p1)^3 * p3 * p4 * p4 * p4 * p5 * p24
3^3 * 
929 * 
1753 * 
2503 * 
4049 * 
11171 * 

527360168663641090261567

 27...7654321
35
83
3.216.341.629
7.350.476.679.347
571.747.168.838.911.343

Rsm27 = (p1)^5 * p2 * p10 * p13 * p18
3^5 * 
83 * 

3216341629 * 

7350476679347 * 

571747168838911343

 28...7654321
23
193
3.061
2.150.553.615.963.932.561
967.536.566.438.740.710.859

Rsm28 = p2 * p3 * p4 * p19 * p21
23 * 
193 * 
3061 * 

2150553615963932561 * 

967536566438740710859

 29...7654321
3
11
709
105.971
2.901.761
1.004.030.749
405.373.772.791.370.720.522.747

Rsm29 = p1 * p2 * p3 * p6 * p7 * p10 * p24
3 * 
11 * 
709 * 

105971 * 

2901761 * 

1004030749 * 

405373772791370720522747

 30...7654321
3
73
79
18.041
24.019
32.749
5.882.899.163
209.731.482.181.889.469.325.577

Rsm30 = p1 * p2 * p2 * p5 * p5 * p5 * p10 * p24
3 * 
73 * 
79 * 

18041 * 
24019 * 
32749 * 

5882899163 * 

209731482181889469325577

 31...7654321
7
30.331.061
147.434.568.678.270.777.660.714.676.905.519.165.947.
    320.523

Rsm31 = p1 * p8 * p45
7 * 

30331061 * 

147434568678270777660714676905519165947320523

 32...7654321
3
17
1.231
28.409
103.168.496.413
17.560.884.933.793.586.444.909.640.307.424.273

Rsm32 = p1 * p2 * p4 * p5 * p12 * p35
3 * 
17 * 
1231 * 

28409 * 

103168496413 * 

17560884933793586444909640307424273

 33...7654321
3
7
7.349
9.087.576.403
237.602.044.832.357.211.422.193.379.947.758.321.446.
    883

Rsm33 = p1 * p1 * p4 * p10 * p42
3 * 
7 * 
7349 * 

9087576403 * 

237602044832357211422193379947758321446883

 34...7654321
89
488.401
2.480.227
63.292.783
254.189.857
3.397.595.519
5.826.028.611.726.606.163

Rsm34 = p2 * p6 * p7 * p8 * p9 * p10 * p19
89 * 
488401 * 
2480227 * 
63292783 * 

254189857 * 

3397595519 * 

5826028611726606163

 35...7654321
32
881
1.559
755.173
7.558.043
1.341.824.123
4.898.857.788.363.449
7.620.732.563.980.787

Rsm35 = p(1)^2 * p3 * p4 * p6 * p7 * p10 * p16 * p16
3^2 * 
881 * 
1559 * 
755173 * 
7558043 * 

1341824123 * 

4898857788363449 * 

7620732563980787

 36...7654321
32
112
971
1.114.060.688.051
1.110.675.649.582.997.517.457
277.844.768.201.513.190.628.337

Rsm36 = p(1)^2 * (p2)^2 * p3 * p13 * p22 * p24
3^2 * 
11^2 * 
971 * 

1114060688051 * 

1110675649582997517457 * 

277844768201513190628337

 37...7654321
29
2.549.993
39.692.035.358.805.460.481
12.729.390.074.866.695.790.994.160.335.919.964.253

Rsm37 = p2 * p7 * p20 * p38
29 * 
2549993 * 

39692035358805460481 * 

12729390074866695790994160335919964253

 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

Rsm38 = p1 * p4 * p63
3 * 
9833 * 

130084529452972348314460579180389918709759033057100685484626179

 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

Rsm39 = p1 * p2 * p2 * p3 * p5 * p58
3 * 
19 * 
73 * 
709 * 
66877 * 

1996163827266702824413525236841223322799723697285999656577

 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

Rsm40 = p2 * p2 * p3 * p27 * p39
11 * 
41 * 
199 * 

537093776870934671843838337 * 

837983319570695890931247363677891299117

 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

Rsm41 = p1 * p2 * p2 * p2 * p7 * p14 * p20 * p28
3 * 
29 * 
41 * 
89 * 
3506939 * 

18697991901857 * 

59610008384758528597 * 

3336615596121104783654504257

 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

Rsm42 = p1 * p5 * p5 * p5 * p10 * p52
3 * 
13249 * 
14159 * 
25073 * 

6372186599 * 

4717130738223261316867440830358870217018600625280851

 43...7654321
52.433
73.638.227.044.684.393.717
11.246.650.506.151.248.047.514.771.323.412.217.987.
   665.845.460.131.261

Rsm43 = p5 * p20 * p53
52433 * 

73638227044684393717 * 

11246650506151248047514771323412217987665845460131261

 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

Rsm44 = (p1)^2 * p1 * p4 * p6 * p6 * p23 * p41
3^2 * 
7 * 
3067 * 
114883 * 
245653 * 

65711907088437660760939 * 

12400566709419342558189822382901899879241

 45...7654321
32
23
167
15.859
25.578.743
32.406.938.830.550.964.081.541.672.531.706.672.083.
   265.765.131.138.228.893.759.713.957

Rsm45 = (p1)^2 * p2 * p3 * p5 * p8 * p65
3^2 * 
23 * 
167 * 
15859 * 
25578743 * 

32406938830550964081541672531706672083265765131138228893759713957

 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

Rsm46 = p2 * p5 * p12 * p23 * p43
23 * 
35801 * 

543124946137 * 

45223810713458070167393 * 

2296875006922250004364885782761014060363847

 47...7654321
3
11
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

Rsm47 = p1 * p2 * p2 * p2 * p16 * p28 * p38
3 * 
11 * 
31 * 
59 * 

1102254985918193 * 

4808421217563961987019820401 * 

14837375734178761287247720129329493021

 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

Rsm48 = p1 * p3 * p3 * p6 * p15 * p24 * p38
3 * 
151 * 
457 * 
990013 * 

246201595862687 * 

636339569791857481119613 * 

15096613901856713607801144951616772467

 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

Rsm49 = p2 * p10 * p77
71 * 

9777943361 * 

71279637669169187180216178143931072216235463059085052636143589860866110201991

 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

Rsm50 = p1 * p3 * p4 * p13 * p30 * p43
3 * 
157 * 
3307 * 

3267926640703 * 

771765128032466758284258631297 * 

1285388803256371775298530192200584446319323

 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

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

Rsm52 = p1 * p2 * p6 * p12 * p14 * p16 * p47
7 * 
29 * 
670001 * 

403520574901 * 

70216544961751 * 

1033003489172581 * 

13191839603253798296021585972083396625125257997

 53...7654321
34
499
673
6.287
57.653
199.236.731
1.200.017.544.380.023
1.101.541.941.540.576.883.505.692.003
2.061.265.130.010.645.250.941.617.446.327

Rsm53 = (p1)^4 * p3 * p3 * p4 * p5 * p9 * p16 * p28 * p31
3^4 * 
499 * 
673 * 
6287 * 

57653 * 

199236731 * 

1200017544380023 * 

1101541941540576883505692003 * 

2061265130010645250941617446327

 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

Rsm54 = (p1)^3 * (p1)^4 * p2 * p4 * p9 * p11 * p13 * p15 * p43
3^3 * 
7^4 * 
13 * 
1427 * 

632778317 * 

57307460723 * 

7103977527461 * 

617151073326209 * 

2852320009960390860973654975784742937560247

 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

Rsm55 = p9 * p9 * p84

357274517 * 

460033621 * 

337952850450733861795390882190470745732440551509303900198252202379628657263082856953

 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

Rsm56 = p1 * (p2)^2 * p14 * p87
3 * 
13^2 * 

85221254605693 * 

130893658529726305450095097258014177208962504037645212881820251999576244730152822433471

 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

Rsm57 = p1 * p2 * p11 * p93
3 * 
41 * 

25251380689 * 

185341405391688249727709433589302205214498999971321371212688202452892497774826168815604386643

 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

Rsm58 = p2 * p7 * p15 * p18 * p28 * p40
11 * 

2425477 * 

178510299010259 * 

377938364291219561 * 

5465728965823437480371566249 * 

5953809889369952598561290100301076499293

 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

Rsm59 = p1 * p31 * p78
3 * 

8878987335542530798199706004667 * 

223695767334983176713475674533908530446231765827709335846079166299801865160321

 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

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

Rsm61 = p2 * p3 * p22 * p42 * p46
13 * 
373 * 

6399032721246153065183 * 

214955646066967157613788969151925052620751 * 

9236498149999681623847165427334133265556780913

 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

Rsm62 = (p1)^2 * p2 * p3 * p7 * p13 * p14 * p28 * p50
3^2 * 
11 * 
487 * 
6870011 * 

3921939670009 * 

11729917979119 * 

9383645385096969812494171823 * 

43792191037915584824808714186111429193335785529359

 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

Rsm63 = (p1)^2 * p2 * p5 * p24 * p86
3^2 * 
97 * 

26347 * 

338856918508353449187667 * 

81634539084915174560475674776787544426426157020315628260064812816949080776530011946073

 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

Rsm64 = p3 * p3 * p12 * p14 * p24 * p65
397 * 
653 * 

459162927787 * 

27937903937681 * 

386877715040952336040363 * 

50238676722181090702078407150521845843639197722581325849647297921

 65...7654321  (by Philippe Strohl)
3
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

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


 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

Rsm66 = p1 * p2 * p2 * p4 * p7 * p7 * p103
3 * 
53 * 
83 * 
2857 * 
1154129 * 
9123787 * 

1678909630451355851720548638776904129368032732116932059545601625238248196366270162621578014348386071863

 67...7654321  (by Philippe Strohl)
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

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

Step 2 took 277257ms

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

Found probable prime factor of 40 digits: 7606472255743608789748570171445062146361

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

 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

Rsm68 = p1 * p2 * p6 * p8 * p9 * p18 * p20 * p67
3 * 
29 * 
277213 * 

68019179 * 

152806439 * 

295650514394629363 * 

14246700953701310411 * 

6504446830680818400791682931901597157630284650677644922374842962527

 69...7654321
3
11
71
167
1.481
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

Rsm69 = p1 * p2 * p2 * p3 * p4 * p10 * p23 * p89
3 * 
11 * 
71 * 
167 * 
1481 * 

2326583863 * 

19962002424322006111361 * 

25893078065197846051718991595178434426254383595503019580054933145462167064671076549357327

 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

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

Rsm71 = (p1)^2 * p2 * p3 * p5 * p10 * p11 * p19 * p87
3^2 * 
17 * 
131 * 
16871 * 

1504047269 * 

82122861127 * 

1187275015543580261 * 

144604206245872959501627508393777181764477823520160883196217868977782582373557713248699

 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

Rsm72 = (p1)^2 * p3 * p4 * p129
3^2 * 
449 * 
1279 * 

140694452786937519168991180114261899104420602632532713737057441161711270533237275941788793148690589619459960576436357556531306839

 73...7654321
7
11
21.352.291
1.051.174.717
92.584.510.595.404.843
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

Rsm73 = p1 * p2 * p8 * p10 * p17 * p20 * p83
7 * 
11 * 

21352291 * 

1051174717 * 

92584510595404843 * 

33601392386546341921 * 

13712664395603610315522432764639471643768450652229502858089980699747050646322820953

 74...7654321
3
177.337
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

Rsm74 = p1 * p6 * p10 * p11 * p15 * p16 * p32 * p51
3 * 
177337 * 

6647068667 * 

31386093419 * 

669035576309897 * 

4313244765554839 * 

67415094145569534144512937880453 * 

346129598050812738223913038086154784537962590242993

 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

Rsm75 = p1 * p1 * p6 * p7 * p8 * p10 * p14 * p17 * p28 * p53
3 * 
7 * 
230849 * 
7341571 * 
24260351 * 

1618133873 * 

19753258488427 * 

46752975870227777 * 

7784620088430169828319398031 * 

75410934119527447300390571688926480400272241123206797

 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

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

rlambda: 2.4

alambda: 2.4

qintsize: 1000

Factor base limits: 6000000/6000000

Large primes per side: 3

Large prime bits: 29/29

Sieved special-q in [1200000, 17401001)

Relations: rels:16524456, finalFF:924466

Initial matrix: 825292 x 924466 with sparse part having

weight 120427251.

Pruned matrix : 799012 x 803202 with weight 96263252.

Total sieving time: 217.75 hours.

Total relation processing time: 5.41 hours.

Matrix solve time: 25.40 hours.

Time per square root: 0.37 hours.

Prototype def-par.txt line would be:

snfs,146,5,0,0,0,0,0,0,0,0,6000000,6000000,29,29,50,50,2.4,

2.4,100000

total time: 248.93 hours.

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

AMD XP 2400+

 77...7654321  (by Robert Backstrom)
3
919
571.664.356.244.249
6.547.011.663.195.178.496.329
591.901.089.382.359.628.031.506.373
335.808.390.273.971.395.786.635.145.251.293
3.791.725.400.705.852.972.336.277.620.397.793.613.
  760.330.637

Rsm77 = p1 * p3 * p15 * p22 * p27 * p33 * p46    ( Robert Backstrom )
3 * 
919 * 

571664356244249 * 

6547011663195178496329 * 

591901089382359628031506373 * 

335808390273971395786635145251293 * 

3791725400705852972336277620397793613760330637

 78...7654321  (by Robert Backstrom)
3
17
47
17.795.025.122.047
78.119.581.556.663.469.779.307.447.735.538.451.582.
   384.717.692.143.654.960.846.437 
236.415.864.091.491.721.631.173.832.082.837.638.453.
    438.349.732.083.245.678.426.495.346.687 

Rsm78 = p1 * p2 * p2 * p14 * p62 * p69    ( Robert Backstrom )
3 * 
17 * 

47 * 

17795025122047 * 

78119581556663469779307447735538451582384717692143654960846437 * 

236415864091491721631173832082837638453438349732083245678426495346687


Summary file for Rsm78(c131)

Number: n

N=184687083761843541748388950977995441256600712441278871226437494245

63274925368143110340183242396198894897040039760682794559283704219

  ( 131 digits)

SNFS difficulty: 150 digits.

Divisors found:

 r1=78119581556663469779307447735538451582384717692143654960846437

(pp62)

 r2=236415864091491721631173832082837638453438349732083245678426495346

687 (pp69)

Version: GGNFS-0.77.1

Total time: 229.19 hours.

Scaled time: 315.82 units (timescale=1.378).

Factorization parameters were as follows:

name: Rsm78

n:

18468708376184354174838895097799544125660071244127887122643749424563

274925368143110340183242396198894897040039760682794559283704219

skew: 50.0

type: snfs

deg: 5

c5: 772100

c0: 8790000000121

m:  100000000000000000000000000000

rlim: 5500000

alim: 5500000

lpbr: 29

lpba: 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,150,5,0,0,0,0,0,0,0,0,5500000,5500000,29,29,50,50,2.5,2.5,100000

total time: 229.19 hours.

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

Athlon 64, 3200+ running Cygwin.

 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

Rsm79 = p6 * p15 * p19 * p112
160591 * 

274591434968167 * 

1050894390053076193 * 

1721746072956576690202206138718569810869766278855728135524979427336961475483160058092704761582299124638700313801

 80...7654321  (by Philippe Strohl)
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

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

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

863833301651529343619738144943149594546456312503049126604455097

2970223270768917110223269 has 88 digits

 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

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

23^2 * 

62273 * 

22193 * 

352409 * 

914359181934271 * 

128616475245109794691881271516023399420747375754647255684774783381708606008286190288296622667517228900357838852877964197

 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

Rsm82 = PRIME!

  82818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321



 83...7654321  (by Philippe Strohl)
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

Rsm83 = p1 * p28 * p130    ( Philippe Strohl )
3 * 

1974871757105304370241687597 * 

1414913491576959991085772193821333363948491052493852298827038471195985672820912298157918486848781698715932375003792034192407725831
RESULTS (all the probable primes have been verified primes by apr-cl)

Line=21/35 Curves=15/1100 B1=1000000 factors=0

C157  Using  B1=1000000,  B2=839549780,  polynomial Dickson(6),

sigma=3334714852

Step 1 took 167057ms

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

Found probable prime factor of 28 digits:

1974871757105304370241687597

Probable prime cofactor

141491349157695999108577219382133336394849105249385229882703847

119598567282091229815791848684878169871593237500379203419240772

5831 has 130 digits



 84...7654321  (by Philippe Strohl)
3
11
47
83
447.841
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

Rsm84 = p1 * p2 * p2 * p2 * p6 * p8 * p14 * p34 * p96    ( Philippe Strohl )
3 * 

11 * 

47 * 

83 * 

447841 * 

18360053 * 

53294058577163 * 

9982711074569412202184829872323289 * 

125041734265706422786569078989578766735056823257328035341596020039345650335832474986014272849361
RESULTS (all the probable primes have been verified primes by apr-cl)

Line=22/35 Curves=34/1100 B1=1000000 factors=2

C130  Using  B1=1000000,  B2=839549780,  polynomial Dickson(6),

sigma=198298906

Step 1 took 122862ms

Step 2 took 83545ms

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

9982711074569412202184829872323289

Found probable prime factor of 34 digits:

9982711074569412202184829872323289

Probable prime cofactor

125041734265706422786569078989578766735056823257328035341596020

039345650335832474986014272849361 has 96 digits



 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

Rsm85 = p12 * p22 * p128

465619934881 * 

5013354844603778080337 * 

36776645009790287118723906169819493438565519545996236768005404618296375898835476299088296154006135887578611770836159053334073793


 86...7654321  (by Philippe Strohl)
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

Rsm86 = p1 * p1 * p4 * p6 * p8 * p8 * p35 * p104    ( Philippe Strohl )
3 * 

7 * 

3761 * 

205111 * 

16080557 * 

16505767 * 

32250226453787273178911188574002189 * 

62637021423581274124666903882920660177315636462243958664624625942830414280475868522207254411510840826741
RESULTS (all the probable primes have been verified primes by apr-cl)

Line=17/27 Curves=74/1000 B1=1000000 factors=0

C139  Using  B1=1000000,  B2=839549780,  polynomial Dickson(6),

sigma=1952017108

Step 1 took 20761ms

Step 2 took 11392ms

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

32250226453787273178911188574002189

Found probable prime factor of 35 digits:

32250226453787273178911188574002189

Probable prime cofactor

626370214235812741246669038829206601773156364622439586646246259

42830414280475868522207254411510840826741 has 104 digits



 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

Rsm87 = p1 * p4 * p25 * p30 * p107
3 * 

2423 * 

4433139632126658657934801 * 

951802198132419645688492825211 * 

28648431477796086247464902964197486005683397987974560052454771919641592769777638753833612094955143339736919

 88...7654321
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

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



 89...7654321
 
32
19
7.052.207
7.453.913.650.365.787.997.832.333.663.083.262.488.
  621.192.563.938.875.862.741.184.541.290.967.573.
  359.240.174.460.309.117.965.435.974.246.994.708.
  201.602.646.981.680.832.171.393.417.817.854.901.
  687.876.167.491.293 = c160

Rsm89 = (p1)^2 * p2 * p7 * c160

3^2 *

19 * 

7052207 * 

7453913650365787997832333663083262488621192563938875862741184541290967573359240174460309117965435974246994708201602646981680832171393417817854901687876167491293

Rsm90 (COMPLETE) by Philippe Strohl

3^2
157
257
691
23710539556091113372464330404686919 (p35)
2656628283592678268561853393086924912569196381871916529968854546224536796760248847319073272592288758864393 (p106)


Rsm91 (COMPLETE) by Philippe Strohl

11
29
163
3559
2297
22899893
350542343218231
8365221234379371317434883
4297948891268072885236875337601 (p31)
65641960036224024756000092194722617 (p35)
11412914421079678469007301289508708061707176282507 (p50)

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(All rights reserved) - Last modified : December 11, 2007.

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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com

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