mersenneforum.org Odd perfect related road blocks II
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 2011-09-28, 06:12 #562 debrouxl     Sep 2009 977 Posts Thanks to both of you For now, other persons can still join the fun; in a few days, all tasks are likely to be reserved. In other news, the factorization of 4933^53-1 is completed by: prp66 factor: 682124495314218121698509554279455063384319487036254811177607644173 prp125 factor: 15087546736509299281340920554482138392768250520514664644614948251205819917930670495559070714562075103199392808634768628382131 (RSALS + Lionel Debroux) Last fiddled with by wblipp on 2011-10-22 at 00:53 Reason: Fix exponent
 2011-10-19, 21:36 #563 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 19·337 Posts I have done post-processing for 173^109-1 2467^71-1 4099^67-1 571^89-1 It was a useful opportunity to sort out how to run MPI msieve reasonably efficiently; 571^89-1 took 234844 seconds (65h14m) on 24 CPUs to solve a 10942652 x 10942830 matrix for an SNFS-difficulty-245.3 number. I would be intrigued to know what these factorisations have done for the proof, and where the road-blocks currently lie. Last fiddled with by fivemack on 2011-10-19 at 21:36
 2011-10-22, 11:31 #564 Pascal Ochem     Apr 2006 101 Posts Let $\Omega(N)$ be the number of distinct prime factors and $\omega(N)$ be the total number of prime factors of an odd perfect number N. Your numbers are "Brent composites", of the form p^q-1 with p<10000. They appear when we get around roadblocks in the proof of $N > 10^{1500}$. RSALS is sieving those with SNFS difficulty between 200 and 250 digits. Here are the 100 most difficult composites for the lower bounds on N. http://www.lirmm.fr/~ochem/opn/mostwantedrb.txt It might soon be out of date, check the factordb before starting sieving. The format for p^q-1 is "p q-1 composite weight", where "weight" is the number of roadblocks involving the composite. The worst is $6115909044841454629^{17}-1$ (where $6115909044841454629=(11^ {19}-1)/10$) both for the lower bounds on N and $\omega(N)$. It is also the only roadblock for the lower bound on $\omega(N)-2\Omega(N)$, in another paper in preparation. I guess this one won't be done in the near future, but others are interesting and too small for RSALS, for example: 163^89-1 C195 weight=163041 1021^61-1 C181 weight=43074 1229^59-1 C180 weight=34178 2237^53-1 C175 weight=15846
2011-10-23, 13:06   #565
em99010pepe

Sep 2004

2×5×283 Posts

Quote:
 Originally Posted by Pascal Ochem I guess this one won't be done in the near future, but others are interesting and too small for RSALS, for example: 163^89-1 C195 weight=163041 1021^61-1 C181 weight=43074 1229^59-1 C180 weight=34178 2237^53-1 C175 weight=15846
Are those ones still available? 2237^53-1 was on my list a few months ago given to me by William.

Carlos

 2011-10-23, 14:32 #566 chris2be8     Sep 2009 2,063 Posts How much ECM have the C1nn had? I could do a few if you want. Chris K
2011-10-23, 19:21   #567
wblipp

"William"
May 2003
New Haven

22×3×197 Posts

Quote:
Originally Posted by em99010pepe
Quote:
 Originally Posted by Pascal Ochem but others are interesting and too small for RSALS, for example: 163^89-1 C195 weight=163041 1021^61-1 C181 weight=43074 1229^59-1 C180 weight=34178 2237^53-1 C175 weight=15846
Are those ones still available?
163^89-1 is at the very bottom end of the RSALS range, and is at the top of the RSALS queue. It has had more than 2/9 ECM. If anybody wants it, please speak up soon or it will go to RSALS.

The other three are indeed too small for RSALS, but have all had sufficient ECM to begin SNFS. I have others from the most wanted roadblocks that are below RSALS range and ready. I was planning on canvassing for interest in these, but had a shortage of round tuits. Is there interest in these 150-200 digit SNFS numbers? Does anyone else have interest in coordinating the work?

 2011-10-23, 21:04 #568 em99010pepe     Sep 2004 B0E16 Posts I'll do 2237^53-1.
2011-10-23, 22:32   #569
wblipp

"William"
May 2003
New Haven

22·3·197 Posts

Quote:
 Originally Posted by Pascal Ochem Here are the 100 most difficult composites for the lower bounds on N. http://www.lirmm.fr/~ochem/opn/mostwantedrb.txt
523^73-1 is factored in the factordb

 2011-10-24, 16:59 #570 chris2be8     Sep 2009 2,063 Posts I'll do 1229^59-1. Chris K
2011-10-25, 16:57   #571
chris2be8

Sep 2009

2,063 Posts

Quote:
 Originally Posted by chris2be8 I'll do 1229^59-1. Chris K
That's about half way through. I'll do 1021^61-1 after that.

Chris K

2011-10-26, 14:25   #572
wblipp

"William"
May 2003
New Haven

1001001111002 Posts

Quote:
 Originally Posted by Pascal Ochem Here are the 100 most difficult composites for the lower bounds on N. http://www.lirmm.fr/~ochem/opn/mostwantedrb.txt It might soon be out of date, check the factordb before starting sieving. The format for p^q-1 is "p q-1 composite weight", where "weight" is the number of roadblocks involving the composite.
The following numbers from the 100 Most Wanted Roadblocks have had ECM to at least 2/9 of the SNFS difficulty, and are ready for SNFS factoring. Only the first one is large enough for RSALS.

163^89-1 C195 weight=163041
853^67-1 C194 weight=38851
1301^59-1 C181 weight=29908
1381^61-1 C189 weight=24140
1361^61-1 C189 weight=24014
1481^61-1 C191 weight=20179
1487^61-1 C191 weight=19585
1489^61-1 C191 weight=19439
2269^53-1 C175 weight=15620

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