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Reversed Smarandache Concatenated Numbers.
Prime factors from n (n=2,3,...,200) downto 1
rood Normal Smarandache Concatenated Numbers
rood Repunits Factorization rood comments


Itinerary


rsm1rsm2rsm3rsm4rsm5rsm6rsm7rsm8rsm9rsm10rsm11rsm12rsm13rsm14rsm15rsm16rsm17rsm18rsm19rsm20
rsm21rsm22rsm23rsm24rsm25rsm26rsm27rsm28rsm29rsm30rsm31rsm32rsm33rsm34rsm35rsm36rsm37rsm38rsm39rsm40
rsm41rsm42rsm43rsm44rsm45rsm46rsm47rsm48rsm49rsm50rsm51rsm52rsm53rsm54rsm55rsm56rsm57rsm58rsm59rsm60
rsm61rsm62rsm63rsm64rsm65rsm66rsm67rsm68rsm69rsm70rsm71rsm72rsm73rsm74rsm75rsm76rsm77rsm78rsm79rsm80
rsm81rsm82rsm83rsm84rsm85rsm86rsm87rsm88rsm89rsm90rsm91rsm92rsm93rsm94rsm95rsm96rsm97rsm98rsm99rsm100
rsm101rsm102rsm103rsm104rsm105rsm106rsm107rsm108rsm109rsm110rsm111rsm112rsm113rsm114rsm115rsm116rsm117rsm118rsm119rsm120
rsm121rsm122rsm123rsm124rsm125rsm126rsm127rsm128rsm129rsm130rsm131rsm132rsm133rsm134rsm135rsm136rsm137rsm138rsm139rsm140
rsm141rsm142rsm143rsm144rsm145rsm146rsm147rsm148rsm149rsm150rsm151rsm152rsm153rsm154rsm155rsm156rsm157rsm158rsm159rsm160
rsm161rsm162rsm163rsm164rsm165rsm166rsm167rsm168rsm169rsm170rsm171rsm172rsm173rsm174rsm175rsm176rsm177rsm178rsm179rsm180
rsm181rsm182rsm183rsm184rsm185rsm186rsm187rsm188rsm189rsm190rsm191rsm192rsm193rsm194rsm195rsm196rsm197rsm198rsm199rsm200

Legend
rsm_Nif N less than 107 - complete factorization is given on this page
rsm_Nif N is above 107 - refer for the complete factorization to M. Fleuren page
rsm_Nfirst Rsm with unknown factors
rsm_NRsm with unknown factors (ref. M. Fleuren's page)
rsm_NRsm with new complete factorization : see list at end of page
rsm_NRsm with a new factor but still incomplete : consult Messages section
rsm_NRsm 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 Numbers by Dr. M. L. Perez
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).


Some Factorization Websites

Factorization using the Elliptic Curve Method
GGNFS - A Number Field Sieve implementation


Messages

[ April 9, 2010 ]
Eric Weisstein (email)

rsm37765

A176024 - Reverse concatenation of the first a(n) integers gives a prime.
Consecutive Number Sequences
Message 10253 - New reverse consecutive integer (probable) prime with 177,719 digits

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
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 ! [ 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)

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 (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

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
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

Done on a i7 Quad with 3.4GHz, 8 threads.

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.

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
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






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E-mail address : pdg@worldofnumbers.com