Odd perfect related road blocks II - Page 52

debrouxl · 2011-09-28, 06:12

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)

fivemack · 2011-10-19, 21:36

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.

Pascal Ochem · 2011-10-22, 11:31

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It might soon be out of date, check the factordb before starting sieving.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

em99010pepe · 2011-10-23, 13:06

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

chris2be8 · 2011-10-23, 14:32

How much ECM have the C1nn had? I could do a few if you want.

Chris K

wblipp · 2011-10-23, 19:21

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?

em99010pepe · 2011-10-23, 21:04

I'll do 2237^53-1.

wblipp · 2011-10-23, 22:32

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

chris2be8 · 2011-10-24, 16:59

I'll do 1229^59-1.

Chris K

chris2be8 · 2011-10-25, 16:57

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

wblipp · 2011-10-26, 14:25

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

2011-09-28, 06:12	#562
debrouxl Sep 2009 1111010001₂ 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 6422₁₀ 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

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2011-10-22, 11:31	#564
Pascal Ochem Apr 2006 103 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, 14:32	#566
chris2be8 Sep 2009 4046₈ Posts	How much ECM have the C1nn had? I could do a few if you want. Chris K

2011-10-23, 21:04	#568
em99010pepe Sep 2004 2·5·283 Posts	I'll do 2237^53-1.

2011-10-24, 16:59	#570
chris2be8 Sep 2009 2·7·149 Posts	I'll do 1229^59-1. Chris K