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

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rsm_N if N less than 107 - complete factorization is given on this page if N is above 107 - refer for the complete factorization to M. Fleuren page first Rsm with unknown factors Rsm with unknown factors (ref. M. Fleuren's page) Rsm with new complete factorization : see list at end of page Rsm with a new factor but still incomplete : consult Messages section Rsm is prime !

Prefatory Notes & Sources

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

The first one with an unknown prime factor is when n = 107.
If there is a breaktrough in completely factorising Rsm107, please let me know,
so that I can update the list.

For the factorizations I also followed the source from
Micha Fleuren, Reversed Smarandache factors

Other subject related sources on the web

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

Book sources

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

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

OEIS entries

A000422 - Concatenation of numbers from n down to 1.
A050677 - Number of prime factors of concatenation of numbers from n down to 1, with multiplicity.
A050678 - First occurrence of n in A050677.
A050679 - Positions of 2's in A050677.
A050680 - Positions of 3's in A050677.
A050681 - Positions of 4's in A050677.
A050682 - Positions of 5's in A050677.
A050687 - A050677(n) is squarefree.
A050688 - Numbers n such that A050677(n) is powerful(1).

PrimeForm or PFGW

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

Some Factorization Websites

Messages

[ April 9, 2010 ]
Eric Weisstein (email)

 rsm37765

After ~12 years of on-and-off searching using spare CPU cycles, it seems I've found only the second known reverse consecutive integer (probable) prime. And it's a big one:

37765 37764 37763 ... 5 4 3 2 1

(spaces denote concatenation here; not multiplication) with 177719 decimal digits. The only previously known such prime was the 155-digit number:

82 81 80 ... 5 4 3 2 1

-Eric

[ 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: 82514915741623328517650484573901437176111
P131: 79276466536870215660589427037258187228232511168042181233242100341381290510746535680251722466853314074942409563489786970760805952371
B1: 3000000
Sigma: 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.

Rsm89
P50: 49388406496643388078114888189038555500608342769177
P111: 150924360170891168648756251949784084919713735816964351919278654382818389528776733970746808714702822077767563109

Rsm92
P43: 5493464474242305396221143000161670754181497
P84: 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 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

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 ! [ 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 5.0
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 ! [ go to 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)
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)
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  (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

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  (by Greg Childers)
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.
776.733.970.746.808.714.702.822.077.767.563.109

Rsm89 = (p1)^2 * p2 * p7 * p50 * p111    ( Greg Childers )
3^2 *
19 *
7052207 *
49388406496643388078114888189038555500608342769177 *
150924360170891168648756251949784084919713735816964351919278654382818389528776733970746808714702822077767563109

Summary for Rsm89(c160) = p50 * p111
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

90...7654321  (by Philippe Strohl)
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

Rsm90 = (p1)^2 * p3 * p3 * p3 * p23 * p35 * p106    ( Philippe Strohl )
3^2 *
157 *
257 *
691 *
57508628219582769985073 *
23710539556091113372464330404686919 *
2656628283592678268561853393086924912569196381871916529968854546224536796760248847319073272592288758864393

91...7654321  (by Philippe Strohl)
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
65.641.960.036.224.024.756.000.092.194.722.617
11.412.914.421.079.678.469.007.301.289.508.708.061.
707.176.282.507

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

92...7654321  (by Greg Childers)
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

Rsm92 = p1 * p2 * p3 * p6 * p7 * p7 * p27 * p43 * p84    ( Greg Childers )
3 *
17 *
113 *
376589 *
3269443 *
6872137 *
125940177196545564166916551 *
5493464474242305396221143000161670754181497 *
275430796569999455663492846893637583669272814955746117769050223296905117622304550539

Summary for Rsm92(c127) = p43 * p84
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

93...7654321  (by Greg Childers)
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

Rsm93 = p1 * p2 * p5 * p8 * p78 * p87    ( Greg Childers )
3 *
13 *
69317 *
14992267 *
201432592198523828197360557776679304467257143112125068672607007837316638653123 *
115053322906328924099643594573730121414771889862698591137393328485987955147846747640987

Summary for Rsm93(c164) = p78 * p87
This was completed by SNFS with Franke's lattice sieve and msieve.
Submitted on Sat, 5 Jul 2008 13:58 AM

94...7654321  (by Sean A. Irvine)
7
593
18.307
51.079.607.083
205.194.325.589.871.744.331.343.573.535.573.305.675.
610.614.816.772.010.742.161
119.196.410.929.996.763.224.260.829.337.602.875.017.
316.813.583.413.263.802.810.338.642.523.016.254.
964.208.346.568.290.970.868.509.031

Rsm94 = p1 * p3 * p5 * p11 * p60 * p102    ( Sean A. Irvine )
7 *
593 *
18307 *
51079607083 *
205194325589871744331343573535573305675610614816772010742161 *
119196410929996763224260829337602875017316813583413263802810338642523016254964208346568290970868509031

Summary for Rsm94(c161) = p60 * p102
by SNFS, 4 days
Submitted on Sun, 1 Sep 2013 02:15 AM

95...7654321  (by Greg Childers)
3
11
13
53
157
623.541.439
1.925.519.505.985.194.246.675.568.556.102.548.265.
695.431.323
2.238.701.414.548.422.437.837.954.711.909.075.778.
087.984.958.846.007.800.228.926.253.371.628.662.
089.310.781.325.800.164.276.662.804.549.907.023.
877.567.116.977

Rsm95 = p1 * p2 * p2 * p2 * p3 * p9 * p46 * p121    ( Greg Childers )
3 *
11 *
13 *
53 *
157 *
623541439 *
1925519505985194246675568556102548265695431323 *
2238701414548422437837954711909075778087984958846007800228926253371628662089310781325800164276662804549907023877567116977

Summary for Rsm95(c166) = p46 * p121
ECM
B1: 11000000
Sigma: 451237925
Submitted on Mon, 2 June 2008 06:50

96...7654321  (by Greg Childers)
3
7
211
2.297
14.563
82.514.915.741.623.328.517.650.484.573.901.437.176.
111
933.668.601.639.537.603.239.754.327.658.420.915.210.
640.646.159.004.272.796.359.399.491.722.404.669.
330.495.677.171.183.756.102.624.389.829

Rsm96 = p1 * p1 * p3 * p4 * p5 * p41 * p105    ( Greg Childers )
3 *
7 *
211 *
2297 *
14563 *
82514915741623328517650484573901437176111 *
79276466536870215660589427037258187228232511168042181233242100341381290510746535680251722466853314074942409563489786970760805952371

Summary for Rsm96(c172) = p41 * p131
ECM
B1: 3000000
Sigma: 2833338313
Submitted on Sun, 1 June 2008 22:49

97...7654321  (by Sean A. Irvine)
1.553
8.442.802.537.257.437.470.685.592.335.103.115.524.
514.594.473.239
7.471.937.400.213.894.534.072.143.066.413.215.379.
587.453.021.367.951.298.017.763.286.207.244.428.
043.224.971.911.962.016.772.935.291.633.993.371.
737.173.377.866.774.627.571.463

Rsm97 = p4 * p49 * p133    ( Sean A. Irvine )
1553 *
8442802537257437470685592335103115524514594473239 *
7471937400213894534072143066413215379587453021367951298017763286207244428043224971911962016772935291633993371737173377866774627571463

Summary for Rsm97(c182) = p49 * p133
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=66351652
Step 1 took 661383ms
Step 2 took 201105ms
********** Factor found in step 2: 8442802537257437470685592335103115524514594473239
Found probable prime factor of 49 digits
Probable prime cofactor has 133 digits
Submitted on Sun, 3 Sep 2013 22:32 PM

98...7654321
32
101
401
5.741
375.373
12.600.485.572.048.377.667.847.602.373.953.825.070.
307.929.745.429.222.391.170.029.103.716.305.319.
173.089.828.544.778.803.098.535.484.577.313.142.
694.214.333.060.282.257.233.501.332.679.141.608.
359.528.879.231.913.951.750.102.333

Rsm98 = p1 * p1 * p3 * p3 * p4 * p6 * p173
3^2 *
101 *
401 *
5741 *
375373 *
12600485572048377667847602373953825070307929745429222391170029103716305319173089828544778803098535484577313142694214333060282257233501332679141608359528879231913951750102333

99...7654321  (by Sean A. Irvine)
32
109
41.829.209
174.489.586.693
4.718.163.853.873.186.702.174.593.648.074.382.889.
452.215.982.857.198.133.601
29.598.145.037.563.819.265.130.550.262.202.805.739.
844.764.945.970.590.686.094.265.029.358.994.243.
381.720.555.167.904.232.167.269.142.884.946.193

Rsm99 = p1 * p1 * p3 * p8 * p12 * p58 * p110 [ Length = 189 ]    ( Sean A. Irvine )
3^2 *
109 *
41829209 *
174489586693 *
4718163853873186702174593648074382889452215982857198133601 *
29598145037563819265130550262202805739844764945970590686094265029358994243381720555167904232167269142884946193

Summary for Rsm99(c168) = p58 * p110
by SNFS, 5 days
Submitted on Fri, 4 Oct 2013 10:40 AM

100...7654321  (by Greg Childers)
13
6.779
48.856.332.919
41.858.129.936.073.024.200.781.901
600.231.117.377.832.784.458.721.416.049.204.359.605.
450.473
933.668.601.639.537.603.239.754.327.658.420.915.210.
640.646.159.004.272.796.359.399.491.722.404.669.
330.495.677.171.183.756.102.624.389.829

Rsm100 = p2 * p4 * p11 * p25 * p45 * p105 [ Length = 192 ]    ( Greg Childers )
13 *
6779 *
48856332919 *
41858129936073024200781901 *
600231117377832784458721416049204359605450473 *
933668601639537603239754327658420915210640646159004272796359399491722404669330495677171183756102624389829

Summary for Rsm100(c150) = p45 * p105
ECM hit pay dirt again...
B1: 11000000
Sigma: 3643562351
Submitted on Mon, 2 June 2008 04:30 AM

101...7654321
3
16.320.902.651
3.845.388.775.716.560.041
527.081.483.440.118.646.719.817.083
693.173.763.848.292.948.494.434.792.706.137
4.951.247.955.407.738.381.292.611.334.774.789.854.
716.423
296.835.073.564.365.810.874.060.326.747.640.395.964.
982.137.371.402.743.968.481.269

Rsm101 = p1 * p11 * p19 * p27 * p33 * p43 * p63 [ Length = 195 ]
3 *
16320902651 *
3845388775716560041 *
527081483440118646719817083 *
693173763848292948494434792706137 *
4951247955407738381292611334774789854716423 *
296835073564365810874060326747640395964982137371402743968481269

Summary for Rsm101(c132) = p27 * p43 * p63
Prime p43 reported by Sean A. Irvine (Source from factordb.com)
Composite Rsm101(c90) = p27 * p63 (re)found by Patrick De Geest using ECM.
Factorization complete in 0d 2h 53m 22s
ECM: 728946791 modular multiplications
Prime checking: 155371 modular multiplications
SIQS: 5225880 polynomials sieved
357770 sets of trial divisions
17646 smooth congruences found (1 out of every 31690522 values)
198942 partial congruences found (1 out of every 2810924 values)
19311 useful partial congruences
Timings:
Primality test of 3 numbers: 0d 0h 0m 0.1s
Factoring 1 number using ECM: 0d 0h 15m 5.6s
Factoring 1 number using SIQS: 0d 2h 38m 16.8s
Submitted on Fri, 4 Oct 2013 10:40 AM

102...7654321
3
101
103
36.749
10.189.033.219
23.663.501.701.518.727.831
52.648.894.306.108.287.380.398.039
304.839.988.680.063.197.179.666.559.481.610.853.243.
020.744.749.329.600.760.379
23.005.509.977.477.707.989.660.194.279.442.389.109.
457.209.390.894.388.457.715.525.672.841.600.109

Rsm102 = p1 * p2 * p2 * p5 * p11 * p20 * p26 * p60 * p74 [ Length = 198 ]
3 *
101 *
103 *
36749 *
10189033219 *
23663501701518727831 *
52648894306108287380398039 *
304839988680063197179666559481610853243020744749329600760379 *
23005509977477707989660194279442389109457209390894388457715525672841600109

Summary for Rsm102(c133) = p60 * p74
Reported by Sean A. Irvine (Source from factordb.com)
Submitted on Fri, 4 Oct 2013 10:40 AM

103...7654321  (by Karsten Bonath)
19
29
103
3.119
154.009.291
329.279.243.129
1.240.336.674.347
22.633.393.225.636.817.509.048.253.413.614.523.936.
779.379.142.819.839
409.131.376.630.520.058.579.639.289.003.992.488.556.
153.028.051.803.583.697.309.565.513.083.246.532.
054.725.642.239.647.211.160.951.734.870.369

Rsm103 = p2 * p2 * p3 * p4 * p9 * p12 * p13 * p53 * p108 [ Length = 201 ]    ( Karsten Bonath )
19 *
29 *
103 *
3119 *
154009291 *
329279243129 *
1240336674347 *
22633393225636817509048253413614523936779379142819839 *
409131376630520058579639289003992488556153028051803583697309565513083246532054725642239647211160951734870369

Summary for Rsm103(c160) = p53 * p108
Hi Patrick,
here's the next found, not expected so fast.
I've done some ecm-work over night and found this:
prp53 = 22633393225636817509048253413614523936779379142819839
(curve 50 stg2 B1=260000000 sigma=4172026601 thread=1)
Finished 400 curves using Lenstra ECM method on C160 input, B1=260M, B2=gmp-ecm Default
The same machine as last found (i7; 3,4GHz, 8 threads).
A ggnfs-run would have taken about 7 days I think and such found so fast was unexpected.
I'm running more ecm on RSm 105, the C156 first before sieving.
Best regards. Karsten Bonath
Submitted on Fri, 17 Jan 2014 10:34 AM

104...7654321  (by Karsten Bonath)
3
7
60.953
1.890.719
10.446.899.741
216.816.630.080.837
1.614.245.774.588.631.629
1.833.458.663.261.756.711.022.474.752.934.885.996.
283.994.068.934.623
6.416.548.836.582.984.645.230.931.997.866.943.915.
126.359.911.365.501.017.028.302.184.124.340.167.
653.853.103.670.734.138.954.937

Rsm104 = p1 * p1 * p5 * p7 * p11 * p15 * p19 * p52 * p97 [ Length = 204 ]    ( Karsten Bonath )
3 *
7 *
60953 *
1890719 *
10446899741 *
216816630080837 *
1614245774588631629 *
1833458663261756711022474752934885996283994068934623 *
6416548836582984645230931997866943915126359911365501017028302184124340167653853103670734138954937

Summary for Rsm104(c149) = p52 * p97
N = 1176447705267521923577368279614902919686503140270320287540598598157407407330617847054552785968064978/
5707601022086721229097737346342594380466196083751 (149 digits)
Divisors found:
r1=1833458663261756711022474752934885996283994068934623 (pp52)
r2=6416548836582984645230931997866943915126359911365501017028302184124340167653853103670734138954937 (pp97)
Version: Msieve v. 1.52 (SVN 927)
Total time: 85.26 hours.
Factorization parameters were as follows:
n: 1176447705267521923577368279614902919686503140270320287540598598157407407330617847054552785968064978/
5707601022086721229097737346342594380466196083751
# norm 2.505044e-014 alpha -6.813456 e 6.561e-012 rroots 3
skew: 6462294.74
c0: -2502915676002659065336605570573371200
c1: -5784562480717262961828330234612
c2: -1517585441166316763157468
c3: 387113785406523795
c4: -77257848482
c5: 552
Y0: -116339584882563246166841092383
Y1: 7655850935767691
type: gnfs
Factor base limits: 19700000/19700000
Large primes per side: 3
Large prime bits: 29/29
Sieved algebraic special-q in [0, 0)
Total raw relations: 43092961
Relations: 6600178 relations
Pruned matrix : 3909682 x 3909914
Polynomial selection time: 0.77 hours.
Total sieving time: 77.04 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.96 hours.
time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,148,5,65,2000,1e-05,0.28,250,20,50000,3600,19700000,19700000,29,29,58,58,2.6,2.6,100000
total time: 85.26 hours.
Intel64 Family 6 Model 58 Stepping 9, GenuineIntel
processors: 8, speed: 3.39GHz
Windows-7-6.1.7601-SP1
Running Python 2.7
Best regards
Karsten Bonath
Submitted on Tue, 14 Jan 2014 09:21 AM

105...7654321  (by Karsten Bonath)
3
7
859
6.047
63.601
20.519.675.652.486.419.201.698.765.330.684.950.547
505.609.049.620.430.043.564.818.948.424.594.740.095.
377.638.674.786.008.583.783.558.052.966.689
1.460.218.912.197.798.897.796.479.876.892.816.487.
811.802.580.775.089.126.778.648.005.904.642.208.
642.833.062.339

Rsm105 = p1 * p1 * p3 * p4 * p5 * p38 * p72 * p85 [ Length = 207 ]    ( Karsten Bonath )
3 *
7 *
859 *
6047 *
63601 *
20519675652486419201698765330684950547 *
505609049620430043564818948424594740095377638674786008583783558052966689 *
1460218912197798897796479876892816487811802580775089126778648005904642208642833062339

Summary for Rsm105(c156) = p72 * p85
Hi there,
here's the next one: C156 of Reverse Smarandache for n=105
The factor P38 = 20519675652486419201698765330684950547 was known before (March 2013).
The remaining C156 factors into
N = 7382998964341072839171792912259030454792371993112679501173854242970557861655134900173907400873767275408904/
36999505780654584253275861736565755273053827425571 (156 digits)
Divisors found:
r1=505609049620430043564818948424594740095377638674786008583783558052966689 (pp72)
r2=1460218912197798897796479876892816487811802580775089126778648005904642208642833062339 (pp85)
Version: Msieve v. 1.52 (SVN 927)
Total time: 334.34 hours.
Factorization parameters were as follows:
n: 7382998964341072839171792912259030454792371993112679501173854242970557861655134900173907400873767275408904/
36999505780654584253275861736565755273053827425571
# norm 4.041748e-015 alpha -7.690727 e 2.242e-012 rroots 5
skew: 166229298.88
c0: -1160217253311944686318415618937046188509715
c1: 104564273776348072754492542431508653
c2: -1358648098004033743541386979
c3: -3186433090234526077
c4: 41382717330
c5: 108
Y0: -5847381565577706707202573659996
Y1: 66086485037964307
type: gnfs
Factor base limits: 28600000/28600000
Large primes per side: 3
Large prime bits: 29/29
Sieved algebraic special-q in [0, 0)
Total raw relations: 63837901
Relations: 6330620 relations
Pruned matrix : 4583792 x 4584019
Polynomial selection time: 1.44 hours.
Total sieving time: 321.91 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 10.33 hours.
time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,155,5,65,2000,1e-05,0.28,250,20,50000,3600,28600000,28600000,29,29,58,58,2.6,2.6,100000
total time: 334.34 hours.
Intel64 Family 6 Model 58 Stepping 9, GenuineIntel
processors: 8, speed: 3.39GHz
Windows-7-6.1.7601-SP1
Running Python 2.7
Best regards.
K.Bonath
Submitted on Tue, 4 Feb 2014 09:26 AM

106...7654321  (by Sean A. Irvine)
1.912.037.972.972.539.041.647
3.052.818.746.214.722.908.609
414.338.872.062.791.501.547.344.020.582.712.133.249.
557
43.871.558.577.296.772.025.736.976.053.227.175.068.
325.706.197.701.002.055.248.304.277.569.975.777.
948.248.915.189.631.633.909.304.741.312.836.729.
962.564.905.149.411

Rsm106 = p22 * p22 * p42 * p125 [ Length = 210 ]    ( Sean A. Irvine )
1912037972972539041647 *
3052818746214722908609 *
414338872062791501547344020582712133249557 *
43871558577296772025736976053227175068325706197701002055248304277569975777948248915189631633909304741312836729962564905149411

Summary for Rsm106(c167) = p42 * p125
Hi Patrick,
Good progress on these numbers in the last few months.
Input number is
181776920965538303686757377254635804562897081317122615583938506926665329668634371684250474607181245/
72874681287411912149791448198810931545176347119222043777538034560927 (167 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=2318285213
Step 1 took 434355ms
Step 2 took 41233ms
********** Factor found in step 2: 414338872062791501547344020582712133249557
Found probable prime factor of 42 digits: 414338872062791501547344020582712133249557
Probable prime cofactor 43871558577296772025736976053227175068325706197701002055248304277569975777948248915189631633909304741312836729962564905149411 has 125 digits
Sean.
Submitted on Sat, 15 Feb 2014 19:33 PM

107...7654321  (by ?)
33
13
4.519
114.967
1.425.213.859
17.641.437.858.251
23.360.253.634.978.845.923.690.492.010.342.796.065.
659.594.873.493.579.746.825.873.590.464.324.228.
231.160.961.116.256.105.969.373.967.177.504.537.
562.091.173.744.655.625.679.325.439.819.496.281.
128.526.415.820.510.882.470.643.939.603.503 = c179

Rsm107 = p1 * p1 * p1 * p2 * p4 * p6 * p10 * p14 * c179 [ Length = 213 ]    ( ? )
3^3 *
13 *
4519 *
114967 *
1425213859 *
17641437858251 *
23360253634978845923690492010342796065659594873493579746825873590464324228231160961116256105969373967177504537562091173744655625679325439819496281128526415820510882470643939603503

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

```

In the Queue
```
Rsm108  3^3.23.457.1373
p12: 605434593221(MF)
p12: 703136513561(MF)
p183: 65173196387249475977416657515202494191651200932587245757641555410
5317494666624168424170710931607986869296093272869434490385792356172937249973308
538912363697035449119378064503710617061

Rsm109  11.29.31^2.1709.30345569
p14: 42304411918757(MF)
p189: 16222580595863552703143293624354404245779294361744688081610853299
3116936260511568560345613293332092205872265638628004044018226045165658419395231
460143420504841063735216158204619725937348527

Rsm110* 3.11.19.53.229.24672421
p24: 611592384837948878235019(AM)
c183: 95889381149763103961458058603078786567854186593508539777966408448
1308829191613853343342295098157173457474970353410015363351379162273337581635009
172220566257867287469102739527750373221

Rsm111* 3.61.269.470077.143063.544035253
c200: 61691713279795800698033099575903185256290114583509505195703427386
0949351632142347294373298680682963411313174163172282552455011549914200020830375
62799829904225569038630441943956331206996087904580258341

Rsm112* 137
p12: 262756224547(MF)
c214: 31144048909982157692842251909214568838383874701103546073259311861
9532587526642335336356545866254933398955131066735984793414074172273889704777538
7141669529366489044798699340682649545577859980470235111194379299262339

Rsm113* 3.19.45061.111211
c219: 39599133335314612123511969259722234992296286416580612594622857852
5185426168530631048073009025379365137986080214904846005578130028567646410500713
687110938599972399522330919672919315127895884606174730415836638041023594543

Rsm114* 3.19.53.59
c228: 64022527118705843899543369355250031195249693389156115998709200516
7156899925652538547005917766355700644475658344506896000659821692085657714375165
0844357657664339686622671657916299644370924897055371850280354983012480512857517
77039

Rsm115* 137.509.1720003
c226: 95975640251096842488762443259456943370853360200051169481124595570
4018396696346412210869696724008356357780532702460829350532898939665301241246079
7114413414808881231353371618452693935299346599060378436747553801062370565829924
79

Rsm116  3^2.83.103.156307.176089.21769127
p217: 25187163357041407592248409402110540642992232623701999604725418643
1273479196596824755688535207751737578846956063492250849199208807587907687003937
3549798736261002573575973195504651252447990869047840482800158103798979961

Rsm117  3^2
p242: 13012901679345901345678901012011900678344900344677900111099774399
4376991009987642984275980908977541974174970807967440964073960706957339953972950
6059472389438719405049371379337709304039270369236699203029169359135689102019068
3490346790109739369

Rsm118  7.4603
p241: 36658426527765777943611653924182398779089756402067627044784425675
6757826547621082147313393075379658569804653715673538055515553721598527686783699
0023442863817059828883474858761068676867990885858021257200975303135291021978886
941789923376400101

Rsm119* 3.7
c247: 56722912912435768625291481481004337193860050049572905762429047570
4617118758532899947041361182775324189465603607017748431889846031260172674314088
4555025969167383308797450211591625733039874454015868157282298696440110581524722
938864353005767189888301

Rsm120* 3.73
c249: 54848912382244801421969457584981784980870824705526987717854384018
2182509565932839767072505414832798256072090304828647156030579304413537151879479
2629025367367694751118024952257690600017983441257275490013832341215764489598722
33706466444808772196290659

Rsm121* 31.371177
c248: 10526246552759075477607901795927037514500134324760033544825810093
1239828428602873572019843136037826647540713154046719449408990508456374708141817
3991406548806298156118800505718682369555020518750540754386906298406043697284168
5913274982725084825725783

Rsm122* 3.17
p11: 91673873887(MF)
c245: 26120111057956427779065998930134485067649174219123823723750216996
5371583528489515350264985786198630030899659412736583429608694550911813155880680
6733865473990392452907519064420982317528588637831236469377699222439041512982959
4143741035572004632533

Rsm123  3.1197997
p11: 15744706711(MF)
p244: 21758278358874055599464828420428042323499641923630303222513180445
8373638183180661242661938260877481451308962893881178713838701073141408697099915
2622906040282361053830375023371428063409895341689611948425812573204125450386130
956923032776792888721

Rsm124* 37.1223
c259: 27429918039627879851962855210959782792007051801973018741266514353
9594928512076855692901680165983047620352806308850809457861168755888644884903464
1546844525114551626605939150848588644371493302338962538670162744099164724056321
965090765110587207269483837287816571

Rsm125  3^2.59.83
p10: 5961006911(MF)
p13: 1096598255677(MF)
p240: 43431142834343211424792195820186942025276000732342903799063088081
9097497984186829313004351475996086338529303064166192171643009311576430811848218
6759786220014787748199754534276867406483710064883571726322903725817016977014257
16260473441585091

Rsm126* 3^2.13.68879.135342173
c255: 11563672052769784020484123601804437698325084918040802614222816991
3194568720299026287507868881940245339975545101745516046644465293430081732353339
5850678274877198784875493522261364537771729079380565817106617425106104349262721
71743281269197312590622174389439

Rsm127* 97
p16: 1385409249340483(AM)
c255: 94598661742076339684862899520697167229887105127861543330850948309
7785854730046185788743125586346370905486693204808433087619112779208534703896744
3858398384258480522767355384670090801651501894960926520534477297785027522102275
41308298710077584078015123882971

Rsm128* 3.34613.29497667
c263: 41830486872601614043131496303543741355201700860187162246175639054
6548190806157415896590358289507894008449376171531050917475329362169591352199084
5677494436392269133260747440592740303039450600235117364781537447130093765909129
3708250497052966882113137846681530433317

Rsm129* 3.23.1213.82507
p12: 420130412231(MF)
c257: 44507791411901419389750599498079616439793553651721504435341243038
6003295048215519806319122297824101956355608684937776904906909559810579801646647
8284181336396794547012023833548551312930330541713326454997753291508627972873391
0978175503420277344628674173218629

```