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 completely factorized first Rsm with unknown factors Rsm with unknown factors 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 factorizing Rsm107, please let me know,
so that I can update the list.

For the factorization 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 (some sequences for illustration purpose)

A000422 - Concatenation of numbers from n down to 1.
A038395 - Concatenation of the first n odd numbers in reverse order.
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).
A083453 - a(n) = (concatenation of numbers from n to 1) - n^n.
A104759 - Concatenation of digits of natural numbers from n down to 1.
A116504 - Number of distinct prime divisors of the concatenation of n,...,1.
A138793 - a(n) = concatenation of reversed digits of natural numbers from n down to 1.
A272617 - Concatenation of the numbers from n down to 1 with numbers from 1 to n.

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 factorization 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 factorization 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
Rsm1 = p1 [ Length = 1 ] unity

1

21
Rsm2 = p1 * p1 [ Length = 2 ]

3
7

321
Rsm3 = p1 * p3 [ Length = 3 ]

3
107

4321
Rsm4 = p2 * p3 [ Length = 4 ]

29
149

54321
Rsm5 = p1 * p2 * p3 [ Length = 5 ]

3 *
19 *
953

654321
Rsm6 = p1 * p6 [ Length = 6 ] semiprime

3 *
218107

7654321
Rsm7 = p2 * p6 [ Length = 7 ] semiprime

19 *
402859

87654321
Rsm8 = (p1)^2 * p4 * p4 [ Length = 8 ]

3^2 *
1997 *
4877

987654321
Rsm9 = (p1)^2 * (p2)^2 * p6 [ Length = 9 ]

3^2 *
17^2 *
379721

10987654321
Rsm10 = p1 * p5 * p5 [ Length = 11 ]

7 *
28843 *
54421

1110987654321
Rsm11 = p1 * p12 [ Length = 13 ] semiprime

3 *
370329218107

12...7654321
Rsm12 = p1 * p1 * p13 [ Length = 15 ]

3 *
7 *
5767189888301

13...7654321
Rsm13 = p2 * p7 * p9 [ Length = 17 ]

17 *
3243967 *
237927839

14...7654321
Rsm14 = p1 * p2 * p8 * p10 [ Length = 19 ]

3 *
11 *
24769177 *
1728836281

15...7654321
Rsm15 = p1 * p2 * (p2)^2 * p2 * p15 [ Length = 21 ]

3 *
13 *
19^2 *
79 *
136133374970881

16...7654321
Rsm16 = p2 * p3 * p4 * p16 [ Length = 23 ]

23 *
233 *
2531 *
1190788477118549

17...7654321
Rsm17 = (p1)^2 * p2 * p5 * p5 * p5 * p9 [ Length = 25 ]

3^2 *
13 *
17929 *
25411 *
47543 *
677181889

18...7654321
Rsm18 = (p1)^2 * (p2)^2 * p2 * p2 * p3 * p3 * p7 * p9 [ Length = 27 ]

3^2 *
11^2 *
19 *
23 *
281 *
397 *
8577529 *
399048049

19...7654321
Rsm19 = p2 * p2 * p13 * p14 [ Length = 29 ]

17 *
19 *
1462095938449 *
40617114482123

20...7654321
Rsm20 = p1 * p2 * p3 * p5 * p21 [ Length = 31 ]

3 *
89 *
317 *
37889 *
629639170774346584751

21...7654321
Rsm21 = p1 * p2 * p12 * p19 [ Length = 33 ]

3 *
37 *
732962679433 *
2605975408790409767

22...7654321
Rsm22 = p2 * p3 * p6 * p13 * p14 [ Length = 35 ]

13 *
137 *
178489 *
1068857874509 *
65372140114441

23...7654321
Rsm23 = p1 * p1 * p3 * p33 [ Length = 37 ]

3 *
7 *
191 *
578960862423763687712072079528211

24...7654321
Rsm24 = p1 * p3 * p3 * p5 * p29 [ Length = 39 ]

3 *
107 *
457 *
57527 *
28714434377387227047074286559

25...7654321
Rsm25 = p2 * p2 * p2 * p9 * p9 * p20 [ Length = 41 ]

11 *
31 *
59 *
158820811 *
410201377 *
19258319708850480997

26...7654321
Rsm26 = (p1)^3 * p3 * p4 * p4 * p4 * p5 * p24 [ Length = 43 ]

3^3 *
929 *
1753 *
2503 *
4049 *
11171 *
527360168663641090261567

27...7654321
Rsm27 = (p1)^5 * p2 * p10 * p13 * p18 [ Length = 45 ]

3^5 *
83 *
3216341629 *
7350476679347 *
571747168838911343

28...7654321
Rsm28 = p2 * p3 * p4 * p19 * p21 [ Length = 47 ]

23 *
193 *
3061 *
2150553615963932561 *
967536566438740710859

29...7654321
Rsm29 = p1 * p2 * p3 * p6 * p7 * p10 * p24 [ Length = 49 ]

3 *
11 *
709 *
105971 *
2901761 *
1004030749 *
405373772791370720522747

30...7654321
Rsm30 = p1 * p2 * p2 * p5 * p5 * p5 * p10 * p24 [ Length = 51 ]

3 *
73 *
79 *
18041 *
24019 *
32749 *
5882899163 *
209731482181889469325577

31...7654321
Rsm31 = p1 * p8 * p45 [ Length = 53 ]

7 *
30331061 *
147434568678270777660714676905519165947320523

32...7654321
Rsm32 = p1 * p2 * p4 * p5 * p12 * p35 [ Length = 55 ]

3 *
17 *
1231 *
28409 *
103168496413 *
17560884933793586444909640307424273

33...7654321
Rsm33 = p1 * p1 * p4 * p10 * p42 [ Length = 57 ]

3 *
7 *
7349 *
9087576403 *
237602044832357211422193379947758321446883

34...7654321
Rsm34 = p2 * p6 * p7 * p8 * p9 * p10 * p19 [ Length = 59 ]

89 *
488401 *
2480227 *
63292783 *
254189857 *
3397595519 *
5826028611726606163

35...7654321
Rsm35 = p(1)^2 * p3 * p4 * p6 * p7 * p10 * p16 * p16 [ Length = 61 ]

3^2 *
881 *
1559 *
755173 *
7558043 *
1341824123 *
4898857788363449 *
7620732563980787

36...7654321
Rsm36 = p(1)^2 * (p2)^2 * p3 * p13 * p22 * p24 [ Length = 63 ]

3^2 *
11^2 *
971 *
1114060688051 *
1110675649582997517457 *
277844768201513190628337

37...7654321
Rsm37 = p2 * p7 * p20 * p38 [ Length = 65 ]

29 *
2549993 *
39692035358805460481 *
12729390074866695790994160335919964253

38...7654321
Rsm38 = p1 * p4 * p63 [ Length = 67 ]

3 *
9833 *
130084529452972348314460579180389918709759033057100685484626179

39...7654321
Rsm39 = p1 * p2 * p2 * p3 * p5 * p58 [ Length = 69 ]

3 *
19 *
73 *
709 *
66877 *
1996163827266702824413525236841223322799723697285999656577

40...7654321
Rsm40 = p2 * p2 * p3 * p27 * p39 [ Length = 71 ]

11 *
41 *
199 *
537093776870934671843838337 *
837983319570695890931247363677891299117

41...7654321
Rsm41 = p1 * p2 * p2 * p2 * p7 * p14 * p20 * p28 [ Length = 73 ]

3 *
29 *
41 *
89 *
3506939 *
18697991901857 *
59610008384758528597 *
3336615596121104783654504257

42...7654321
Rsm42 = p1 * p5 * p5 * p5 * p10 * p52 [ Length = 75 ]

3 *
13249 *
14159 *
25073 *
6372186599 *
4717130738223261316867440830358870217018600625280851

43...7654321
Rsm43 = p5 * p20 * p53 [ Length = 77 ]

52433 *
73638227044684393717 *
11246650506151248047514771323412217987665845460131261

44...7654321
Rsm44 = (p1)^2 * p1 * p4 * p6 * p6 * p23 * p41 [ Length = 79 ]

3^2 *
7 *
3067 *
114883 *
245653 *
65711907088437660760939 *
12400566709419342558189822382901899879241

45...7654321
Rsm45 = (p1)^2 * p2 * p3 * p5 * p8 * p65 [ Length = 81 ]

3^2 *
23 *
167 *
15859 *
25578743 *
32406938830550964081541672531706672083265765131138228893759713957

46...7654321
Rsm46 = p2 * p5 * p12 * p23 * p43 [ Length = 83 ]

23 *
35801 *
543124946137 *
45223810713458070167393 *
2296875006922250004364885782761014060363847

47...7654321
Rsm47 = p1 * p2 * p2 * p2 * p16 * p28 * p38 [ Length = 85 ]

3 *
11 *
31 *
59 *
1102254985918193 *
4808421217563961987019820401 *
14837375734178761287247720129329493021

48...7654321
Rsm48 = p1 * p3 * p3 * p6 * p15 * p24 * p38 [ Length = 87 ]

3 *
151 *
457 *
990013 *
246201595862687 *
636339569791857481119613 *
15096613901856713607801144951616772467

49...7654321
Rsm49 = p2 * p10 * p77 [ Length = 89 ]

71 *
9777943361 *
71279637669169187180216178143931072216235463059085052636143589860866110201991

50...7654321
Rsm50 = p1 * p3 * p4 * p13 * p30 * p43 [ Length = 91 ]

3 *
157 *
3307 *
3267926640703 *
771765128032466758284258631297 *
1285388803256371775298530192200584446319323

51...7654321
Rsm51 = p1 * p2 * p92 [ Length = 93 ]

3 *
11 *
15607560143831952831034557389011016191916100088735534098252188243005506550042821851848110737

52...7654321
Rsm52 = p1 * p2 * p6 * p12 * p14 * p16 * p47 [ Length = 95 ]

7 *
29 *
670001 *
403520574901 *
70216544961751 *
1033003489172581 *
13191839603253798296021585972083396625125257997

53...7654321
Rsm53 = (p1)^4 * p3 * p3 * p4 * p5 * p9 * p16 * p28 * p31 [ Length = 97 ]

3^4 *
499 *
673 *
6287 *
57653 *
199236731 *
1200017544380023 *
1101541941540576883505692003 *
2061265130010645250941617446327

54...7654321
Rsm54 = (p1)^3 * (p1)^4 * p2 * p4 * p9 * p11 * p13 * p15 * p43 [ Length = 99 ]

3^3 *
7^4 *
13 *
1427 *
632778317 *
57307460723 *
7103977527461 *
617151073326209 *
2852320009960390860973654975784742937560247

55...7654321
Rsm55 = p9 * p9 * p84 [ Length = 101 ]

357274517 *
460033621 *
337952850450733861795390882190470745732440551509303900198252202379628657263082856953

56...7654321
Rsm56 = p1 * (p2)^2 * p14 * p87 [ Length = 103 ]

3 *
13^2 *
85221254605693 *
130893658529726305450095097258014177208962504037645212881820251999576244730152822433471

57...7654321
Rsm57 = p1 * p2 * p11 * p93 [ Length = 105 ]

3 *
41 *
25251380689 *
185341405391688249727709433589302205214498999971321371212688202452892497774826168815604386643

58...7654321
Rsm58 = p2 * p7 * p15 * p18 * p28 * p40 [ Length = 107 ]

11 *
2425477 *
178510299010259 *
377938364291219561 *
5465728965823437480371566249 *
5953809889369952598561290100301076499293

59...7654321
Rsm59 = p1 * p31 * p78 [ Length = 109 ]

3 *
8878987335542530798199706004667 *
223695767334983176713475674533908530446231765827709335846079166299801865160321

60...7654321
Rsm60 = p1 * p10 * p101 [ Length = 111 ]

3 *
8522287597 *
23700935879737805587656602711356665465672635558102860173996672149163434889038991753831159994173925831

61...7654321
Rsm61 = p2 * p3 * p22 * p42 * p46 [ Length = 113 ]

13 *
373 *
6399032721246153065183 *
214955646066967157613788969151925052620751 *
9236498149999681623847165427334133265556780913

62...7654321
Rsm62 = (p1)^2 * p2 * p3 * p7 * p13 * p14 * p28 * p50 [ Length = 115 ]

3^2 *
11 *
487 *
6870011 *
3921939670009 *
11729917979119 *
9383645385096969812494171823 *
43792191037915584824808714186111429193335785529359

63...7654321
Rsm63 = (p1)^2 * p2 * p5 * p24 * p86 [ Length = 117 ]

3^2 *
97 *
26347 *
338856918508353449187667 *
81634539084915174560475674776787544426426157020315628260064812816949080776530011946073

64...7654321
Rsm64 = p3 * p3 * p12 * p14 * p24 * p65 [ Length = 119 ]

397 *
653 *
459162927787 *
27937903937681 *
386877715040952336040363 *
50238676722181090702078407150521845843639197722581325849647297921

65...7654321
Rsm65 = p1 * p1 * p2 * p5 *p5 * p31 * p79 [ Length = 121 ]  (by 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
Rsm66 = p1 * p2 * p2 * p4 * p7 * p7 * p103 [ Length = 123 ]

3 *
53 *
83 *
2857 *
1154129 *
9123787 *
1678909630451355851720548638776904129368032732116932059545601625238248196366270162621578014348386071863

67...7654321
Rsm67 = p2 * p11 * p40 * p73 [ Length = 125 ]  (by 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
Rsm68 = p1 * p2 * p6 * p8 * p9 * p18 * p20 * p67 [ Length = 127 ]

3 *
29 *
277213 *
68019179 *
152806439 *
295650514394629363 *
14246700953701310411 *
6504446830680818400791682931901597157630284650677644922374842962527

69...7654321
Rsm69 = p1 * p2 * p2 * p3 * p4 * p10 * p23 * p89 [ Length = 129 ]

3 *
11 *
71 *
167 *
1481 *
2326583863 *
19962002424322006111361 *
25893078065197846051718991595178434426254383595503019580054933145462167064671076549357327

70...7654321
Rsm70 = p7 * p8 * p22 * p96 [ Length = 131 ]

1157237 *
41847137 *
8904924382857569546497 *
163938846357211792847104088800127399738668867423240262451107510450122250847315487025414093609197

71...7654321
Rsm71 = (p1)^2 * p2 * p3 * p5 * p10 * p11 * p19 * p87 [ Length = 133 ]

3^2 *
17 *
131 *
16871 *
1504047269 *
82122861127 *
1187275015543580261 *
144604206245872959501627508393777181764477823520160883196217868977782582373557713248699

72...7654321
Rsm72 = (p1)^2 * p3 * p4 * p129 [ Length = 135 ]

3^2 *
449 *
1279 *
140694452786937519168991180114261899104420602632532713737057441161711270533237275941788793148690589619459960576436357556531306839

73...7654321
Rsm73 = p1 * p2 * p8 * p10 * p17 * p20 * p83 [ Length = 137 ]

7 *
11 *
21352291 *
1051174717 *
92584510595404843 *
33601392386546341921 *
13712664395603610315522432764639471643768450652229502858089980699747050646322820953

74...7654321
Rsm74 = p1 * p6 * p10 * p11 * p15 * p16 * p32 * p51 [ Length = 139 ]

3 *
177337 *
6647068667 *
31386093419 *
669035576309897 *
4313244765554839 *
67415094145569534144512937880453 *
346129598050812738223913038086154784537962590242993

75...7654321
Rsm75 = p1 * p1 * p6 * p7 * p8 * p10 * p14 * p17 * p28 * p53 [ Length = 141 ]

3 *
7 *
230849 *
7341571 *
24260351 *
1618133873 *
19753258488427 *
46752975870227777 *
7784620088430169828319398031 *
75410934119527447300390571688926480400272241123206797

76...7654321
Rsm76 = p2 * p63 * p79 [ Length = 143 ]  (by 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
Rsm77 = p1 * p3 * p15 * p22 * p27 * p33 * p46 [ Length = 145 ]  (by Robert Backstrom )

3 *
919 *
571664356244249 *
6547011663195178496329 *
591901089382359628031506373 *
335808390273971395786635145251293 *
3791725400705852972336277620397793613760330637

78...7654321
Rsm78 = p1 * p2 * p2 * p14 * p62 * p69 [ Length = 147 ]  (by 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
Rsm79 = p6 * p15 * p19 * p112 [ Length = 149 ]

160591 *
274591434968167 *
1050894390053076193 *
1721746072956576690202206138718569810869766278855728135524979427336961475483160058092704761582299124638700313801

80...7654321
Rsm80 = (p1)^3 * p2 * p6 * p7 * p17 * p33 * p88 [ Length = 151 ]  (by 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
Rsm81 = (p1)^3 * (p2)^2 * p5 * p5 * p6 * p15 * p120 [ Length = 153 ]

3^3 *
23^2 *
62273 *
22193 *
352409 *
914359181934271 *
128616475245109794691881271516023399420747375754647255684774783381708606008286190288296622667517228900357838852877964197

82...7654321
Rsm82 = p155 [ Length = 155 ] PRIME!

82818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

83...7654321
Rsm83 = p1 * p28 * p130 [ Length = 157 ]  (by 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
Rsm84 = p1 * p2 * p2 * p2 * p6 * p8 * p14 * p34 * p96 [ Length = 159 ]  (by 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
Rsm85 = p12 * p22 * p128 [ Length = 161 ]

465619934881 *
5013354844603778080337 *
36776645009790287118723906169819493438565519545996236768005404618296375898835476299088296154006135887578611770836159053334073793

86...7654321
Rsm86 = p1 * p1 * p4 * p6 * p8 * p8 * p35 * p104 [ Length = 163 ]  (by 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
Rsm87 = p1 * p4 * p25 * p30 * p107 [ Length = 165 ]

3 *
2423 *
4433139632126658657934801 *
951802198132419645688492825211 *
28648431477796086247464902964197486005683397987974560052454771919641592769777638753833612094955143339736919

88...7654321
Rsm88 = p2 * p4 * p65 * p98 [ Length = 167 ]  (by 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
Rsm89 = (p1)^2 * p2 * p7 * p50 * p111 [ Length = 169 ]  (by 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
Rsm90 = (p1)^2 * p3 * p3 * p3 * p23 * p35 * p106 [ Length = 171 ]  (by Philippe Strohl )

3^2 *
157 *
257 *
691 *
57508628219582769985073 *
23710539556091113372464330404686919 *
2656628283592678268561853393086924912569196381871916529968854546224536796760248847319073272592288758864393

91...7654321
Rsm91 = p2 * p2 * p3 * p4 * p4 * p8 * p15 * p25 * p31 * p35 * p50 [ Length = 173 ]  (by Philippe Strohl )

11 *
29 *
163 *
3559 *
2297 *
22899893 *
350542343218231 *
8365221234379371317434883 *
4297948891268072885236875337601 *
65641960036224024756000092194722617 *
11412914421079678469007301289508708061707176282507

92...7654321
Rsm92 = p1 * p2 * p3 * p6 * p7 * p7 * p27 * p43 * p84 [ Length = 175 ]  (by 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
Rsm93 = p1 * p2 * p5 * p8 * p78 * p87 [ Length = 177 ]  (by 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
Rsm94 = p1 * p3 * p5 * p11 * p60 * p102 [ Length = 179 ]  (by 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
Rsm95 = p1 * p2 * p2 * p2 * p3 * p9 * p46 * p121 [ Length = 181 ]  (by 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
Rsm96 = p1 * p1 * p3 * p4 * p5 * p41 * p105 [ Length = 183 ]  (by 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
Rsm97 = p4 * p49 * p133 [ Length = 185 ]  (by 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
Rsm98 = p1 * p1 * p3 * p3 * p4 * p6 * p173 [ Length = 187 ]

3^2 *
101 *
401 *
5741 *
375373 *
12600485572048377667847602373953825070307929745429222391170029103716305319173089828544778803098535484577313142694214333060282257233501332679141608359528879231913951750102333

99...7654321
Rsm99 = p1 * p1 * p3 * p8 * p12 * p58 * p110 [ Length = 189 ]  (by 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
Rsm100 = p2 * p4 * p11 * p25 * p45 * p105 [ Length = 192 ]  (by 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
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
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
Rsm103 = p2 * p2 * p3 * p4 * p9 * p12 * p13 * p53 * p108 [ Length = 201 ]  (by 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
Rsm104 = p1 * p1 * p5 * p7 * p11 * p15 * p19 * p52 * p97 [ Length = 204 ]  (by 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
Rsm105 = p1 * p1 * p3 * p4 * p5 * p38 * p72 * p85 [ Length = 207 ]  (by 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
Rsm106 = p22 * p22 * p42 * p125 [ Length = 210 ]  (by 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
Rsm107 = (p1)^3 * p2 * p4 * p6 * p10 * p14 * c179 [ Length = 213 ]

3^3 *
13 *
4519 *
114967 *
1425213859 *
17641437858251 *
23360253634978845923690492010342796065659594873493579746825873590464324228231160961116256105969373967177504537562091173744655625679325439819496281128526415820510882470643939603503

108...7654321
Rsm108 = (p1)^3 * p2 * p3 * P4 * p12 * p12 * p183 [ Length = 216 ]

3^3 *
23 *
457 *
1373 *
605434593221 *
703136513561 *
651731963872494759774166575152024941916512009325872457576415554105317494666624168424170710931607986869296093272869434490385792356172937249973308538912363697035449119378064503710617061

109...7654321
Rsm109 = p2 * p2 * (p2)^2 * p4 * p8 * p14 * p189 [ Length = 219 ]

11 *
29 *
31^2 *
1709 *
30345569 *
42304411918757 *
162225805958635527031432936243544042457792943617446880816108532993116936260511568560345613293332092205872265638628004044018226045165658419395231460143420504841063735216158204619725937348527

110...7654321
Rsm110 = p1 * p2 * p2 * p2 * p3 * p8 * p24 * c183 [ Length = 222 ]

3 *
11 *
19 *
53 *
229 *
24672421 *
611592384837948878235019 *
958893811497631039614580586030787865678541865935085397779664084481308829191613853343342295098157173457474970353410015363351379162273337581635009172220566257867287469102739527750373221

111...7654321
Rsm111 = p1 * p2 * p3 * p6 * p6 * p9 * c200 [ Length = 225 ]

3 *
61 *
269 *
470077 *
143063 *
544035253 *
61691713279795800698033099575903185256290114583509505195703427386094935163214234729437329868068296341131317416317228255245501154991420002083037562799829904225569038630441943956331206996087904580258341

112...7654321
Rsm112 = p3 * p12 * c214 [ Length = 228 ]

137 *
262756224547 *
3114404890998215769284225190921456883838387470110354607325931186195325875266423353363565458662549333989551310667359847934140741722738897047775387141669529366489044798699340682649545577859980470235111194379299262339

113...7654321
Rsm113 = p1 * p2 * p5 * p6 * c219 [ Length = 231 ]

3 *
19 *
45061 *
111211 *
395991333353146121235119692597222349922962864165806125946228578525185426168530631048073009025379365137986080214904846005578130028567646410500713687110938599972399522330919672919315127895884606174730415836638041023594543

114...7654321
Rsm114 = p1 * p2 * p2 * p2 * c228 [ Length = 234 ]

3 *
19 *
53 *
59 *
640225271187058438995433693552500311952496933891561159987092005167156899925652538547005917766355700644475658344506896000659821692085657714375165084435765766433968662267165791629964437092489705537185028035498301248051285751777039

115...7654321
Rsm115 = p3 * p3 * p7 * c225 [ Length = 237 ]

137 *
509 *
1720003 *
959756402510968424887624432594569433708533602000511694811245955704018396696346412210869696724008356357780532702460829350532898939665301241246079711441341480888123135337161845269393529934659906037843674755380106237056582992479

116...7654321
Rsm116 = (p1)^2 * p2 * p3 * p6 * p6 * p8 * p217 [ Length = 240 ]

3^2 *
83 *
103 *
156307 *
176089 *
21769127 *
2518716335704140759224840940211054064299223262370199960472541864312734791965968247556885352077517375788469560634922508491992088075879076870039373549798736261002573575973195504651252447990869047840482800158103798979961

117...7654321
Rsm117 = (p1)^2 * p242 [ Length = 243 ]

3^2 *
130129016793459013456789010120119006783449003446779001110997743994376991009987642984275980908977541974174970807967440964073960706957339953972950605947238943871940504937137933770930403927036923669920302916935913568910201906834903467901097393
69

118...7654321
Rsm118 = p1 * p4 * p241 [ Length = 246 ]

7 *
4603 *
366584265277657779436116539241823987790897564020676270447844256756757826547621082147313393075379658569804653715673538055515553721598527686783699002344286381705982888347485876106867686799088585802125720097530313529102197888694178992337640010
1

119...7654321
Rsm119 = p1 * p1 * c247 [ Length = 249 ]

3 *
7 *
567229129124357686252914814810043371938600500495729057624290475704617118758532899947041361182775324189465603607017748431889846031260172674314088455502596916738330879745021159162573303987445401586815728229869644011058152472293886435300576718
9888301

120...7654321
Rsm120 = p1 * p2 * p24 * p37 * c190 [ Length = 252 ]

3 *
73 *
183042452264106470202677 *
1369334368542519718898553975744893377 *
2188299122440995677182085547662523753123006834547810522634204447879310033484532938491801655939766401139209088516807530650240153090195168348581690820539872346355428302871236290370797414023671

p24 and p37 submitted to factordb.com on 8 & 9 December 2021 (communicated by Alex Latham)

121...7654321
Rsm121 = p2 * p6 * c248 [ Length = 255 ]

31 *
371177 *
105262465527590754776079017959270375145001343247600335448258100931239828428602873572019843136037826647540713154046719449408990508456374708141817399140654880629815611880050571868236955502051875054075438690629840604369728416859132749827250848
25725783

122...7654321
Rsm122 = p1 * p2 * p11 * c245 [ Length = 258 ]

3 *
17 *
91673873887 *
261201110579564277790659989301344850676491742191238237237502169965371583528489515350264985786198630030899659412736583429608694550911813155880680673386547399039245290751906442098231752858863783123646937769922243904151298295941437410355720046
32533

123...7654321
Rsm123 = p1 * p7 * p11 * p244 [ Length = 261 ]

3 *
1197997 *
15744706711 *
217582783588740555994648284204280423234996419236303032225131804458373638183180661242661938260877481451308962893881178713838701073141408697099915262290604028236105383037502337142806340989534168961194842581257320412545038613095692303277679288
8721

124...7654321
Rsm124 = (p1)^2 * p1 * p2 * p13 * p40 * c259 [ Length = 264 ]

37 *
1223 *
274299180396278798519628552109597827920070518019730187412665143539594928512076855692901680165983047620352806308850809457861168755888644884903464154684452511455162660593915084858864437149330233896253867016274409916472405632196509076511058720
7269483837287816571

125...7654321
Rsm125 = (p1)^2 * p2 * p2 * p10 * p13 * p240 [ Length = 267 ]

3^2 *
59 *
83 *
5961006911 *
1096598255677 *
434311428343432114247921958201869420252760007323429037990630880819097497984186829313004351475996086338529303064166192171643009311576430811848218675978622001478774819975453427686740648371006488357172632290372581701697701425716260473441585091

126...7654321
Rsm126 = (p1)^2 * p2 * p5 * p9 * c255 [ Length = 270 ]

3^2 *
13 *
68879 *
135342173 *
115636720527697840204841236018044376983250849180408026142228169913194568720299026287507868881940245339975545101745516046644465293430081732353339585067827487719878487549352226136453777172907938056581710661742510610434926272171743281269197312
590622174389439

127...7654321
Rsm127 = p2 * p16 * c255 [ Length = 273 ]

97 *
1385409249340483 *
945986617420763396848628995206971672298871051278615433308509483097785854730046185788743125586346370905486693204808433087619112779208534703896744385839838425848052276735538467009080165150189496092652053447729778502752210227541308298710077584
078015123882971

128...7654321
Rsm128 = p1 * p5 * p8 * c263 [ Length = 276 ]

3 *
34613 *
29497667 *
418304868726016140431314963035437413552017008601871622461756390546548190806157415896590358289507894008449376171531050917475329362169591352199084567749443639226913326074744059274030303945060023511736478153744713009376590912937082504970529668
82113137846681530433317

129...7654321
Rsm129 = p1 * p2 * p4 * p5 * p12 * c257 [ Length = 279 ]

3 *
23 *
1213 *
82507 *
420130412231 *
445077914119014193897505994980796164397935536517215044353412430386003295048215519806319122297824101956355608684937776904906909559810579801646647828418133639679454701202383354855131293033054171332645499775329150862797287339109781755034202773
44628674173218629

130...7654321
Rsm130 = p2 * p3 * p5 * p9 * c264 [ Length = 282 ]

31 *
263 *
86969 *
642520369 *
285631237283639726498886454784844318667595395813081472261629838190978118083572603707635191144827161364516162744796625038595767153158866829462146552960553723109427359147648571398819259646334815327331248465739027480370264628925343431188612282
122164340733809724975537

131...7654321
Rsm131 = p1 * p2 * p4 * p6 * p12 * p23 * c239 [ Length = 285 ]

3 *
11 *
4111 *
852143 *
606617222863 *
33247682213571703426139 *
56240928254556601192103063814942548355506489413422173658716082904570326773802304578210973782155548646383653242130278681756310767702246070706614140532454208674732643079789300907300986679009501197672633732442570958868460730902018819828787917

132...7654321
Rsm132 = p1 * p1 * p2 * p2 * p2 * p5 * p5 * p6 * p6 * p17 * p20 * p226 [ Length = 288 ]

3 *
7 *
11 *
41 *
43 *
31259 *
69317 *
180307 *
199313 *
16995472858509251 *
56602777258539682957 *
4331185773032849081539913623083198503014665722439321484213609427395610421158861149417719649163280953086219160164186357426932838648461333120109868268627872965864578096924580706565898943202208589591489668753779194132906114629087

133...7654321
Rsm133 = p1 * p2 * p20 * p269 [ Length = 291 ]

7 *
13 *
22533511116338912411 *
649250995295906395138092197822115466244903764572660819785073066093266487048948537349718763605137235546669650980139813829942315317247972146602642072403734599996179941805904748351921477755901450765277727412572855336426017537110945345804072334
22483842750678850394225176921

134...7654321
Rsm134 = (p1)^3 * p2 * p8 * p17 * c266 [ Length = 294 ]

3^3 *
37 *
29004967 *
60164048964096599 *
769415880789574080402397212520235416689922699099768110748821582197827857454572288899301748889869009288106672663961950449908721030531235662025041358632308098720107940336010388816833451367971974194178913234049534580387647297577395954570725601
82593718101181805991593063

135...7654321
Rsm135 = (p1)^3 * p3 * p4 * p5 * p12 * p22 * c251 [ Length = 297 ]

3^3 *
211 *
5393 *
98563 *
207481965329 *
6789282931372049267693 *
316789111522656372908791061595849162149759232228294294441993556593526086932083033363256194508325569162008894889407874380387043571793523584607967013854569093793558930273565644542377283534262547558024358111245675810726738897668199801304848946
22607761191

136...7654321
Rsm136 = c300 [ Length = 300 ]

136135134133132131130129128127126125124123122121120119118117116115114113112111110109108107106105104103102101100999897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363
534333231302928272625242322212019181716151413121110987654321

137...7654321
Rsm137 = p1 * p3 * p22 * c278 [ Length = 303 ]

3 *
179 *
6796599525965619205571 *
375738709257150200989339735718004697848745261272620338142990762939313353717615092665103758310365148463445998813453641786815321242227163946360033482535776228633244741983527012081298823883932255082148280549096617773533307020733530085509671359
98580212700260887700217428337557004723

138...7654321
Rsm138 = p1 * p6 * p9 * c292 [ Length = 306 ]

3 *
119611 *
314087617 *
122565222343273699947823149681324384558734400017017349024205806876664663250431801529833433199521055836930891801517695258688153325970304387455403056890909215068598391746483803705927890521360291454911703977574179935808878768410716604568841579
1935756495606374110749969501082015210552091351773761

139...7654321
Rsm139 = p26 * c283 [ Length = 309 ]

53044198312750339053531619 *
262306042059061951008320699056578110640427417489255496424125783509146904476771304646968792922821258812941199573264324302163197375386222671876504449906982390766576701455138361049313104142254636218978173473373404195478112752994038984996956722
2045963122981555058736024981862989957735259

p26 submitted to factordb.com before 4 November 4, 2018 (communicated by Alex Latham)

140...7654321
Rsm140 = p1 * p3 * p6 * p15 * c289 [ Length = 312 ]

3 *
317 *
772477 *
153629260660723 *
124170785173888726613936985380287405432885860003268625210994321197022696583023581360177679171400946176645746695256624547341818792076188063413632279115572880625928957262901045177834424034198178302961372406058266060737319246518155079447803429
3877670919412027103064555316930694384970675986001

141...7654321
Rsm141 = p1 * p3 * p5 * c307 [ Length = 315 ]

3 *
631 *
65831 *
113258153022733575620108145245767526474571212210129347057218109445736794167437253158607095658107747579544379690950713069547941128173163757413353813979692406156161797224715595053306771835590560052640704047426213879133051141955898555064801023
6396754665511613866931585706773170513643049797349087099593829581787

142...7654321
Rsm142 = p3 * p4 * p4 * p4 * p14 * c290 [ Length = 318 ]

859 *
2377 *
2909 *
6521 *
41190901651547 *
890919016717043995227592319178563956995104863104135426009158578108710071526139964562246762234399534025720316347464795166625042751437382910018064271934392063425988411159259891552414973588671510791663294703185448998429597817578158115648067651
13123794428331167260799210696617994164645136256109

143...7654321
Rsm143 = (p1)^2 * p5 * p13 * p302 [ Length = 321 ]

3^2 *
93971 *
9053448211979 *
186946409978496563034913349394559221882962382900720858355004336192863432961505171947498442534939504867021044341030917864308634177820454224458088992446715332498441236785565224160191929844885516055603497637002977567456543617072625990602524732
91623569079262130445817048887079115577109876282386976728239641

144...7654321
Rsm144 = (p1)^2 * p19 * c304 [ Length = 324 ]

3^2 *
5028055908018884749 *
318530759707868200860571655601240161950531451851337521865234632474572569292839424300194115484639608753866240588829805251520359863090083851464865085156893772634713169590305093099357080027341869635535559441585520861072059703519599319852164354
5871786536300804875243000701957474457296150053029881281622850381

145...7654321
Rsm145 = p5 * p7 * p20 * c296 [ Length = 327 ]

57719 *
2691841 *
45690580335973653419 *
204458250228055155327857878905128350512729974118674523822986699528221043521160625508964551160005893920610815703371869649932671795118676876419946169205745577710324947650349812279760598947932012082298012345196807819580297434117718113097861491
41242786601376027094614866371676498629929795789423722821

146...7654321
Rsm146 = p1 * (p1)^2 * p3 * p5 * p5 * p13 * c304 [ Length = 330 ]

3 *
7^2 *
277 *
19319 *
55807 *
2454423915989 *
135632695459905417217582733023425660643726509503468811038106962668322494461998778808527112512646302506693957241737946281996126510650277624853941301840785554624460812490814088913622319822013999421821170673938244472913370312515817916479558951
6990813425882641036496808825055307813425796619972816203808182507

147...7654321
Rsm147 = p1 * (p1)^2 * p2 * p2 * p8 * c321 [ Length = 333 ]

3 *
7^2 *
19 *
31 *
15467623 *
109873429736832043778841619540701349525777028249963990382673960271294309223989512837888341073250550899800456838622952262226626817379889075710582766058437219683774334975731769408786564920716014841636281407541511095532457119174435639289122331
588985588369811380658146059971869639921838308922547470322879428374342167497409169

148...7654321
Rsm148 = p20 * p23 * c294 [ Length = 336 ]

33825333713396366003 *
25082957895838310384953 *
174611342210092022513229749454652353977178135496081007152749016309156120045840661163217930521739969859971072296148584428732478884507774969490668211715832311580810850141920322798280177568261751109460198275856959997188136871183201411327846909
765525240966027409630831385837939365170154873786450019

149...7654321
Rsm149 = p1 * p3 * p8 * c329 [ Length = 339 ]

3 *
109 *
34442413 *
132426999737599893490062332774603640563935216650745509090543309730896154808024397770365702383913648672579746313201075973007482191626110939431795704906929079549666809517893369979557830818852212216864825884270023994392931367540244351941204576
50420977024008689079826485273538899919108910805844376423968603241364303068139239015016771

150...7654321
Rsm150 = p1 * p2 * p3 * c337 [ Length = 342 ]

3 *
59 *
257 *
330077926855165304016670276640814568660856770065585379173275143725138224902998799980483460001580861564589494414282820266680096524669933621543896551036736353619489535798307083006614095382142535733447155922253131901551732653091156678770600751
0728865275452295824187263809363591062396701055930693198977173058153008683839647302675660513772289

151...7654321
Rsm151 = p10 * c335 [ Length = 345 ]

7134941903 *
211844961322801602278364260343355931232083834861374251239130420611259640311504474942776730443014679608270828712190164433510048314556132001212602029370863541563861798406208118369017753564528754955553543176141925941020093079329120693278342954
12013468409108509244822431799894102150173788672870884244245299305451446534647302749894782587007

152...7654321
Rsm152 = (p1)^2 * p2 * p21 * p325 [ Length = 348 ]

3^2 *
13 *
412891312089439668533 *
314958717387652841375546603188043295594311850066041111836703648456186776610661658402868238027976708418411822462956446478593654450959792918705675245104555052978329528219043971336876173143721566560050613576573584831706086980628787494701194709
1875383219429100108486817153716184706777840128072945415968742035741934016878336066361

153...7654321
Rsm153 = (p1)^2 * p5 * p18 * c328 [ Length = 351 ]

3^2 *
67793 *
237333508084627139 *
105763710856844638310560857733893410902303995313405364071990157870271827587462883492305322278932896313513884616531223446121928067038435043558519267091129115042055824728485994761920896250020184651252808057114646901372173878137025190229887705
9043507943835616432365037208950151215830136636869957395559840178643921532425334927804147

154...7654321
Rsm154 = p2 * p5 * p10 * c339 [ Length = 354 ]

11 *
53861 *
1118399729 *
232642072949323434568787876042284231653498293656274622047088779454417957343995846169767877282047238770884145163022635550586651055677523682859844681881430692602345211419342224171343547879619954886891423213430639352528643605780121177943449729
315166203890590541062138488063609934201635642859093503814468387823482822242865225468045572415812519

155...7654321
Rsm155 = p1 * p2 * p8 * c347 [ Length = 357 ]

3 *
41 *
33842293 *
372733573131637891241488788273149510517361616898345871725394922226753687829849566669390482478270181624059690994443673062629550384247316009420491486733990676602131220694863782940637096276377884315656648297764598744955252432016527671882175245
90575353330954262655458357894078941149157358624066593689460865906067685052759193712154912818394492554353239

156...7654321
Rsm156 = p1 * p5 * c355 [ Length = 360 ]

3 *
21961 *
237018888261239092254677455712621078493910632699087988006218806270409867692927052698159050325767078188792436774462483671229475151576449328521939055761131255565325049103867461861131999057863043560370180241310835996824335196444799372671049688
9404493748098273843867846827179234168851668008805615922732169669463007193483487777458862104324055008900826026607587

157...7654321
Rsm157 = p10 * c353 [ Length = 363 ]

4136915059 *
379887314370292832621464150656971819022170895247625001186030242677349431488852164827900393511865250806744016643635223157036824514395022564351641209532765284908655174546819480636326909884806730591827891542523408668516700566748266240316579020
35393141066086839027761518598904123519434933228447546037429376075167133689734351547207419279047658521468185919819

158...7654321
Rsm158 = p1 * p2 * p5 * p10 * p14 * c336 [ Length = 366 ]

3 *
31 *
89209 *
1379633699 *
54957888020501 *
251422070660768338041163557299995474715068503259282481411905145150906503627453467426069097101207319233966623940895568336633486325897045119689413750806808003652098010883381428764448803981610376081057886398569742657060182503344307565679445771
176835994486533264762065083870080686380757300566791629877980107172780878637137335311784298435667

159...7654321
Rsm159 = p1 * p2 * p4 * p5 * p9 * p11 * c340 [ Length = 369 ]

3 *
13 *
5669 *
11213 *
816229087 *
50611041883 *
155409896349382600016635379591884640946363210643109502630368872162399560248953477156322534865593433544417030034232193270559319156619628617486095613143260666423409988794148943683678985540394609124968712170908288854383526535516284203997154773
8261260957780695456322190728004788936365223128711054806658445892772273554511642170255147445317891547

160...7654321
Rsm160 = p1 * p6 * p7 * p21 * c339 [ Length = 372 ]

7 *
942037 *
1223207 *
125729584994875519171 *
157924073193503221612654403363516230001017792995302916786230563519175089723778811788802661842369164144873281229498671435308555949416153658599017723404108493157842057470630824870731647434120304117362265480488233271450997345278627287268588682
590548398887270177970267928057260338097617289337557394501259885887587271155374466527219633767101727

161...7654321
Rsm161 = (p1)^7 * p1 * p2 * p2 * p4 * p6 * p7 * p23 * c328 [ Length = 375 ]

3^7 *
7 *
37 *
67 *
6521 *
826811 *
6018499 *
77558900444266075256801 *
168730679525579392088190271288898574285651392075995470702566881956293563762941917809168794124268916960657437314707639900620843359535183583148556815422068419702762973603199688474986272632216144126082067422948089702461949219320891573772515653
0961463345092675733915359633824019413909814987724683476965741384824090209871593312734019

162...7654321
Rsm162 = (p1)^4 * p7 * p9 * c361 [ Length = 378 ]

3^4 *
1295113 *
202557967 *
763141078874440304134014147976999002848086425871638775805006621349857680860117078230740409035180978906520283621496804710307825873305205650366867391183472916243653991711449741790098714887338413720105723669039416385287456857001117039054398612
5792084779045921753244489867707188704443188153698146375697169691212111268701191719599116916066551653952392853057222470871

163...7654321
Rsm163 = p16 * p17 * c349 [ Length = 381 ]

1139924663537993 *
17672171439068059 *
809940998092214651339777394601480640166988484716250482322212755543853156636438716433561864242121981281763601968465442149688866176648822746748851045128039274376549484251866122092498177967384626811737287155582386121791992067943944751577230284
2829782498950211137605347904377593109441872763471361137911932107675216186618022061381819449521120073575743883

164...7654321
Rsm164 = p1 * p3 * p24 * p358 [ Length = 384 ]

3 *
193 *
105444241520715055381519 *
268889769029932391411612913904512362094878764679844954854956271827159056626396321929239759470989496054401940220261354612023902335789331790372054566319173484753355540425025020499225219196626747717637254052840719433751722336891516671655381844
9317355817786632676689159898141964627324577826646319688844200478228911204272394301977012169335266146111402575366164821

165...7654321
Rsm165 = p1 * c386 [ Length = 387 ]

3 *
550547210540537200530527190520517180510507170500497160490487150480477140470467130460457120450447110440437100430427090420417080410407070400397060390387050380377040370367030360357020350347010340337003332993231983130973029962928952827942726932
62592252491242390232289222188212087201986191885181784171683161582151481141380131279121178111077100976090875080774070673060572050471040370329218107

166...7654321
Rsm166 = p15 * p32 * c344 [ Length = 390 ]

396444477663149 *
15221332593310506150048824812249 *
275362586714883155554069412118902328669060459735245506974708214227899376037423109554149001264429701654396668378104471496574858399175469131367861212952935094476806389160799304547018697488501524631596727473105353540859846459341563025441167391
61692399075902623214316826125720876642971961863203765073008469953774404433878557019909865731569803880221

167...7654321
Rsm167 = p1 * p2 * p3 * p7 * p7 * p9 * p20 * c347 [ Length = 393 ]

3 *
17 *
373 *
7346281 *
8927551 *
194571659 *
68277637362521294401 *
100858250157415737614979315692646754010202732236014226361263160674780778780603838895333514125758512110032725059496110104355594524267091525118502216859935521380364380262322486917224576437608342495148831946642129823477894334033813355709482873
86360781879346479691965499716251665070304697193685759036241688629594777313442667655116190307974031423355563

168...7654321
Rsm168 = p1 * p2 * p5 * p8 * p19 * c362 [ Length = 396 ]

3 *
59 *
35537 *
68102449 *
7766035514845504007 *
505504557265918813789570167865899850932008754588918976109083117167577011684029700376560538892530854888801127790666246647931011798448166870124972905035050240876075320559718425747508980326894439672609485701988797810343990890765784143770515787
08318372669026929294926846289002547847867239407551181378454889908942828149810768977712387589634601361820214763335172958903

169...7654321
Rsm169 = c399 [ Length = 399 ]

169168167166165164163162161160159158157156155154153152151150149148147146145144143142141140139138137136135134133132131130129128127126125124123122121120119118117116115114113112111110109108107106105104103102101100999897969594939291908988878685
848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

170...7654321
Rsm170 = (p1)^2 * p2 * p16 * p384 [ Length = 402 ]

3^2 *
23 *
3737994294192383 *
219923630554256616007719077583019154014155951727854775798517833683934012583941483854765428471116030584150863813731134235805832847629556606343119541057907237377511042714779147697300639653965311160714034657238587710368396139284932119294752077
340314879318837845188251289105890650394156670576557437577233829795047294433461598684394946762835477951525389144355287081866774465666486436275841

171...7654321
Rsm171 = (p1)^2 * p2 * p12 * p19 * p21 * p22 * c330 [ Length = 405 ]

3^2 *
37 *
237089136881 *
2153684224509566597 *
175530075465216996787 *
8105319358780665120301 *
707568504278394542837904831870685614578023302037397142167077037927751324643396404091288089049675424761851078776750118810485917411331336607627199155683156005724210235162607883710505111489358167790091219793666750935632116014900090337100277562
083144474954888386235972577285467808940603729008101420142930565944654316467510179953655943

172...7654321
Rsm172 = p2 * p2 * p3 * p10 * p11 * p15 * p368 [ Length = 408 ]

17 *
29 *
281 *
4631571401 *
31981073881 *
119749047957053 *
700670311933291427306915999093393284487797686466719506754837959929422196747334582196592398017034874043711675725531369700972547827525443593232285933936088439506255320493412307810842864255087305173779407088794957455550935484598024241066576786
18191947134788465411241449252485407758555431338816117444887220147620116525061213520476203375630154851428046066920061015066977409

173...7654321
Rsm173 = p1 * p4 * c407 [ Length = 411 ]

3 *
1787 *
323022143574275635454516256601684689724230850882591225807040017071723839114247616389004186053240330423688002494191634273704779203749541369384678465070179298864241968136760149440615767789798750436687385014185980419888269168065469072178584763
86679514770723443913090801674455786929149542411428197096859094564181245205251355166850353750129346043722036441621774525518173525951360254096627342233939827107090279361

174...7654321
Rsm174 = p1 * p1 * p3 * p3 * p9 * p30 * p370 [ Length = 414 ]

3 *
7 *
269 *
397 *
156894809 *
177303096765665640837873464401 *
279186416437059547864157811919380973192082599963777366522386138355991963952990152425490889319097302694910529921301289667315190668193387159904758070091749159978057768381257876826330958575489129835053802213987260681358086420310067647493151613
0398865371940371234670964603130768541899140710742166290708065761556562341166646588481094875451812350479311651448233532056764510173

p30 submitted to factordb.com before 4 November 4, 2018 (communicated by Alex Latham)

175...7654321
Rsm175 = p1 * p2 * p10 * c405 [ Length = 417 ]

7 *
11 *
3763462823 *
604493619034282928330643489111254048967368046695906177457640889484384271840815021070846594378539465322905826414418396857912771522471869174878704511299207183356478428972091011113360447987311388370946808090691360290217966242626417324700754809
047015769855653610528408625597695095446132827581630648599506214053580231726755845480509961580724161193725011519304060458355175545511791483530165580511189291940200451

176...7654321
Rsm176 = p1 * p2 * p2 * p5 * p13 * p15 * p27 * c358 [ Length = 420 ]

3 *
11 *
47 *
49613 *
2800890701267 *
315698062297249 *
880613122533775176075766757 *
294024954940127443677547225595903226839334354842375567223066624384538126589476489442099850046127966862610511677442401833973600827308997372866050501768658276183590468974008934693036718264373047031848870895016594931379566735286979810621305554
2643743904224240863890376123530951551143396368240680594218001485794293733542622535073690467461319518358341093317107557

177...7654321
Rsm177 = p1 * p2 * p4 * p14 * p404 [ Length = 423 ]

3 *
73 *
1753 *
29988562180903 *
153894694322321330697508204059611852454624045804446965683220353197073865895782846947185456495986054516389107518111869416014367905713716976003597756513247769403595948440108752346179534286253588749037970388622709559871039333495773746415852915
01492794328774400611155615803664451709540042381071386978695045083304738198026053280469054362481201260283231568510236780200113507891888253642492713451299146326920301

178...7654321
Rsm178 = p2 * p2 * p3 * p6 * p6 * p7 * p12 * p14 * p14 * p364 [ Length = 426 ]

13 *
47 *
353 *
644951 *
487703 *
1436731 *
728961984851 *
34686545199997 *
36329334000803 *
199000965342024652337290950824923030839444139915817790324543565714278653899850874397372104760513526457946281223146557763896056535422188538207310941250382470650989108474725045914247024316344452176384640959144209521017800486326875653523319356
7426568792203047526805161997712129040027343983725022440411236007081076773995290702272940784531115358723073473514243267670349

179...7654321
Rsm179 = (p1)^2 * p2 * p2 * p14 * c411 [ Length = 429 ]

3^2 *
23 *
43 *
50981967790529 *
394847796572599893811608382041586040564019704439699194525275899503650059503900758425865332007092437542929961705334460827672530447080688374672515247461898527735456848251732319752661000971813839376254333441231960476354523535247954658473209508
496020064361712447103409230503447764225071332887510296505017608742576745160850382895250328816426597128042713955361984832895866997019502354145082351008558170855528848383549

180...7654321
Rsm180 = (p1)^2 * p2 * p17 * c413 [ Length = 432 ]

3^2 *
29 *
33644294710009721 *
205188334245083063849349291013190126869608797973422236442014997184824820584942460741513809374039964090666908148844181035395475211005548172979367891250078260795400102562778700104030000037609290076371374561669244702574145444528932471134225502
23308853459011650044843847227019690696240010292662076354490683530477775958322306418126460542797154636165474896890020795477022401087120790722145614848381632030764414407907941

181...7654321
Rsm181 = p9 * p17 * c409 [ Length = 435 ]

325251083 *
57421731284347247 *
970098093348404754956312690133221853324023838384809472509391245912671142594206345316713953775405618104858343995557066259830573146712747528278639566155415084418120557083046036122438944356617380807539746818639990500879878831425301939096178395
8707051287673121348041737756691487993218549923867362595965045437760910990375061913417961855289687212057986930362119364903900354468122284809771419347246744454147849165821

182...7654321
Rsm182 = p1 * p3 * p7 * p12 * p417 [ Length = 438 ]

3 *
107 *
5568133 *
139065644033 *
732941018020506002712466637513531371909013827080606297103262435113588759904888234049850275014147565337558330919518668985753472695635401800232779767265330510376425636923300999300108542215006082980842524325204302348982510955287408186238609872
266605082613524266862200346461376464834612161340064650450796403715911045046283385096164530735146655560344349271329589932323720028519791203256447648186642867407601305258119584509

p417 prime cofactor submitted to factordb.com before 4 November 4, 2018 (communicated by Alex Latham)

183...7654321
Rsm183 = p1 * p2 * p2 * c437 [ Length = 441 ]

3 *
23 *
89 *
298293732584561436536681607513716287528366990991967376917707479501972252335382115544952213244019135564483224470194015867355711026119751079852037347555989467726966502406981153110444753496370493598954758371788168234997738332696805255017269343
92298013532160869234586376696288713381971315483279283469756840494011915111035281967861302980940982845716553088267299258500967826761177957557976605313679030821140733157826415759927723727914201430981

184...7654321
Rsm184 = p2 * p5 * p15 * c424 [ Length = 444 ]

23 *
19531 *
196140464783429 *
209040509863004147354993529518106938765422407718895758967814943447124507020805583665081424623045858266827930604675443343959980228481488741977597084408266961595426214618682052733537864923179429898763569415707706523915723897544243265289152144
2974291758715959082978230938330075787343926595673565478833620538643299261422700706757507875298114911090478903415300480726230847000691012526224432645488114794218903138491516988116929473

185...7654321
Rsm185 = p1 * p2 * p3 * p11 * c432 [ Length = 447 ]

3 *
13 *
919 *
32173266383 *
160593741762691092818355442068618320006204521873957045457209149263602235880988138940951601458776376961410541557275548532629236925360320699494051090397303588724042387519520655389831219176784663314558753106992713857256815386506368046495789453
528820074768849739579415931408158249900696821456215412685138273739513323286897072934397803772057911538561918289469805427151930349477702854629329454223081848900007890423378088277614450547534207

186...7654321
Rsm186 = (p1)^2 * p1 * p2 * p13 * p40 * c448 [ Length = 450 ]

3 *
23 *
269833600265481422000259678517646630687207495900246621982850965456759656756755304578490082835007469787177030652390069778472674121946582813246578461068313239324830626277000187142213226268295830611769739303069734950891469729147987116100156676
9653697160914523204362317361878187525969695490995447078011856228808358803967060444882140095139655965303747473268773224855789634006586136581744838222659917872917433743081525251046551002633567411784363927357309

187...7654321
Rsm187 = p2 * p2 * p3 * p3 * p4 * p19 * c423 [ Length = 453 ]

61 *
83 *
103 *
523 *
3187 *
1018598504636281577 *
211417948754778759589979038813379293344995526362816600447773582552258746712138049849968907710401305938916460528673109771369829391199881974886839816375577741944702007733575549481968417314757167325679862688439190685546876821695558821287120413
540956875754414561340454640190904067150003654555886477316318388308201953149508081068917309000717554171288567335409405590282680733604913308361625326411449431519124971285199459443915657

188...7654321
Rsm188 = (p1)^3 * p1 * p4 * p5 * c445 [ Length = 456 ]

3^3 *
7 *
7681 *
65141 *
199001366252072638541372195927418348381844677266270221398820791996462452423661729812797491769246813565639925968036816193671968774605576612906840515050877070793462347392047476902916596345627481543923079952028600604140320598011708271177026742
9233440609754429149975868697457205862891800027724984560432549130580695608364267402474051356003911570211012328975305376266218993579004049577011345809515580812548043136577418979347690337483167083386801507409

189...7654321
Rsm189 = (p1)^3 * p1 * p4 * p4 * p4 * p6 * p8 * c433 [ Length = 459 ]

3^3 *
7 *
2039 *
3823 *
9739 *
212453 *
10586519 *
586246513137593576745855855817333103575968741797901541608276883210825019237818633098615322997631766498829717432189879716371977832136241929518997417133905063655186773359226972363028174539898205752064725437854579440042909728125066215689071684
5663077061364699693422922396803192513297503979821800222241638781692307943824250850672625733858045538995432836344478608836291824706184093544859152545763788128352630203012756311434650066859931069

190...7654321
Rsm190 = (p1)^2 * p1 * p2 * p13 * p40 * c447 [ Length = 462 ]

83 *
107 *
1871 *
25346653 *
451574643566119681937970890871751628632201410756267444653598117589875560210165947992464285325980357094271536289925586272734124085644543385104229413090305736986826127462297396844612528781248626810206856892287498620538215660812692238273795827
724580038095717242932545658190497679312232677971685391484798293748213285369349834978154562400361860530007925739207512271625880472368853107751944854720348613326502914487314456353497780952876761085457001277307

191...7654321
Rsm191 = p1 * p3 * p18 * p444 [ Length = 465 ]

3 *
809 *
627089953107590081 *
125622081102347783528400167144828118450819421050792973603558509598074519808814088971076283652120144666686125402459722943463983477571279433285846993027110347514988070545268828577578471448896705084084971010373940517249706166436432060847778292
911913653361879300601988020373059704015370681356287834238283884746340964587690036002627433956716097105603968925699187301902497382005752927143361840499785428800238959008397401532279354832449017910425194883

192...7654321
Rsm192 = p1 * p4 * c464 [ Length = 468 ]

3 *
2549 *
251328874315663903735040125778974998274067187363902412938633676175193107320736453727166422338382581612603840926056171247747026481167971946052236359543797752242891510575567065691294798131463487809764778508073915420584700038077830673617253972
94639873167138499686949797842696757042108002872969130285328754920712154882021456752684288933402271570140926711734832170257431104425964759389235614810310373236614860384926681473950951781433927333884140078686563542973860466543

193...7654321
Rsm193 = p2 * p3 * p5 * c463 [ Length = 471 ]

47 *
503 *
12049 *
678223323843600969473019732206820114417249017108405051211192655061875548050093082949251317954618633389988069692945939053059783920303758974582150398612006704688074150310021623086853749724232027095766350562358238085317690802821062886787412385
681749577934111753748986560535720003481199143716060435564591058701547049028049027936581887644309919775108582226275252641838258956670640948649820912654734659075530391242525947481547421363444927482348154252366603241960312969

194...7654321
Rsm194 = p1 * p3 * p22 * p23 * c426 [ Length = 474 ]

3 *
179 *
8000103240831609636731 *
77947886830169946060329 *
579908904792091060096773768265189194494639380249059494320012557927739189604988860749467789016408108261972855981439661928224253295492906300662554380050282416650905188786954567117294465373248664291578547083216126561712245373685657346075469180
100829558190577179701743996374189456440801223160661497028044124792299845027414780560276483017210325310641836672920428394434348037242777465292534693181531448005998954491333398743395369667

195...7654321
Rsm195 = p1 * p2 * p4 * c471 [ Length = 477 ]

3 *
79 *
8219 *
100207347692462709995922891019822436837554119060435339016971674243621562352524827554640639788102468738002436547999647393199329819376093753204932764694209693266626798736969519599865155058610789208256329564730444033981221406877611523324373501
203660609954454154087297009710496417995712364065869757359373099837060155910579658423863036192139319808905869900537997305120563809367599749856821676977490535439620671121916151555562229346791358847245084751248917005475196358915773007

196...7654321
Rsm196 = p2 * p16 * c463 [ Length = 480 ]

19 *
8982588119304797 *
114956432546218692573099542271035896518441201291179678686737039708823478297631615986235356683168299272375084511587890465489013693642761743520307162113874313488899231211315701376310188912503583633095657589830074386398106614086253182452154040
2944341442063290775636937715146913050978085569858328855354158399744023602751600130503388234502380988272852759502503270380787554496968513313567250583738837888459884792494637727603939265651181360628213450778322437056259694247

197...7654321
Rsm197 = (p1)^2 * p2 * p2 * p5 * p6 * p6 * p11 * p14 * c440 [ Length = 483 ]

3^2 *
11 *
43 *
11743 *
125201 *
867619 *
61951529111 *
27090970290157 *
216372656995168729648805023716974715959956472937477725581249016798323937589811551599278304295726099666952790720630783887618225424729408478243991396843397412856491521691424196858617006003263177026051637990575392895883208384507833177405676495
19535884845270647037381823767274208510541720808084115150864867545561419510795596743255383858763596963409556411187418445878032497168712331657912386613857944185537329397877994869901990188745017896575967

198...7654321
Rsm198 = (p1)^2 * p2 * p2 * p4 * p19 * p461 [ Length = 486 ]

3^2 *
11 *
37 *
2837 *
1245013373736039779 *
153188878038272629029921163571193360279446153220017095961018727814180705945775832772980487851684429529085761474903007229140673089672285300651668672537166480281890792095768296266030446314704151093571413768851166541136477838070391981894773940
49981878527805353798145721463787576888084900902498901664293146174399595583471539468670614756952798122950219094319036854121572667213685226612386280719390646240730885129275286197568767990359101373643033480326361339423344929

199...7654321
Rsm199 = p3 * p4 * c483 [ Length = 489 ]

103 *
2377 *
813615094478212294166964931688344973419159277967999077654301045121643812160936209761717961243339965797489550600872279899845845326597347370852351831059584563013450686980583104840237303029996757498577112915158334235158648725549967623062933697
608220025716167944880803946845412174549407979806899870118984115156861651258590247921540515083395558894861258408754312855385419601948430801679356681366107039202754082393383368217833500812248180717438980064912634602326551863047229114830724503
791

200...7654321
Rsm108 = p1 * p7 * c485 [ Length = 492 ]

3 *
1666421 *
400457423818663261353109832771730931515679783570466653149036528342634058612589844089363114463410243004151142206687590073097092827797129607212409413449842805125769830763342803013446462286817351149829753171881797637229983953887053199887907719
838142378420811457837111414444709368377112998666211605794896369724693358990993856312398204867094175317601389998400711719248811010076014477057130138133671993956939351829952643906560107747556716928741759141153951342912589739766004941431193200
09967

```