Pascal's OPN roadblock files

[henryzz]

Originally Posted by swellman

I think you can use higher TD, say 90 or 100, but as this job is on the low end of the difficulty spectrum it probably isn’t worth rerunning several times to optimize the matrix size/density and time to solve.

237M for your target number of relations seems high - the mean of the target # rels for 31 and 30 respectively is best for a target # rels for a 31/30 job. Say 190-200M, i.e. (135M+260M)/2.

The usual practice for requesting a 14d job is to post it in this thread.

You can request download credentials from Greg, but if this is a one off then you just rely on a volunteer to run the LA. If no one else steps up I can do it.

Sounds like the sieve region should be altered to 40M-100M. This reduces the estimated relations to 204M. This is still on the high side but I have read large quartics have a higher dup rate.

[Happy5214]

Originally Posted by Pascal Ochem

Thank you!
You might get more hits with this list of composites
https://www.lirmm.fr/~ochem/opn/bound_on_m.txt
They appear in the proof that \(m > 10^{950}\), where \(OPN=p^em^2\)

Originally Posted by Happy5214

Will try, thanks!

Just to update this search... I started with a random shuffle, doing a t30 plus half-a-t35 on each one. I did about 40-ish lines that way, finding 15 factors, and I noticed that most of the factors (12/15) were found with B1=250K or less. I then decided to go from start to finish, doing just under a t30 (yafu is weird about its curve count rounding). I've found a ton of factors doing that through the first 165 lines. In total, I've completely factored six composites and found 63 ECM/P-1 factors so far. I'm trying to post everything to FactorDB as I go.

[henryzz]

Factoring 1528152860898312226820507829734311038694803153043007 ^ 5 - 1 has reduced the proof for 13^4 to 2500 to a third of its previous size(15.6M stat_rec vs 46.4M stat_rec).
Currently have 7/15 of the forbidden primes to 2500. 3 or 4 are nearly there. I believe the first four (127, 19, 7, 11) are going to be the hard ones.

[Happy5214]

Originally Posted by Pascal Ochem

Thank you!
You might get more hits with this list of composites
https://www.lirmm.fr/~ochem/opn/bound_on_m.txt
They appear in the proof that \(m > 10^{950}\), where \(OPN=p^em^2\)

OK, I just finished testing all of these candidates to just under a t30 (that's a t25 + 404 curves @ B1=250K; yafu's rounding was previously mentioned). I eliminated 46 candidates from the list and found a few hundred additional factors (honestly, I lost count). Rather than parse the yafu output, I dumped them into FactorDB as I was going, so you can find them there.