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2020-07-04, 20:09   #771
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT)

26×89 Posts

Quote:
 Originally Posted by Pascal Ochem Yes, it is good to see this one down. Thank you very much, Ryan! No auto-update, I removed the line from the MWRB file. The weight of the remaining composites will be updated in a month or so. 732541 is (29^5-1)/28, so (732541^47-1)/732540 was also a composite of interest for lower bounds on the total number of prime factors.
It is presumably worth waiting for the obvious continuations to be attacked a bit before rerunning the tree. Any before and after statistics on tree size etc would be appreciated.

 2020-07-05, 02:13 #772 ryanp     Jun 2012 Boulder, CO 2·89 Posts In case anyone is interested, here's the full msieve log for 732541^47-1.
 2020-08-02, 20:05 #773 Pascal Ochem     Apr 2006 22·23 Posts The new list of roadblock composites is here http://www.lirmm.fr/~ochem/opn/mwrb2100.txt and the old one is here http://www.lirmm.fr/~ochem/opn/old_mwrb2100.txt Most of the changes are due to the recent factorizations of sigma(3^660) and sigma(732541^46). Notably, the weight of sigma(6115909044841454629^16) drops from 79580833 to 67959517 and the weight of sigma(127^192) drops from 29196565 to 14190689.
 2020-08-03, 16:05 #774 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT) 26·89 Posts Are the files available that contain all the factors used in the proof? How do you check that all the composites hit have been trial factored to at least the assumed level given that pfn doesn't output a file containing the composites hit(I suppose you could extract them from the log)? Does it even matter if there are unfound small factors in non-roadblock composites apart from them causing gcd errors?
2020-08-09, 21:03   #775
Pascal Ochem

Apr 2006

9210 Posts

My policy is to increase the lower bound by a factor 10^100 when the run takes less than one week.
A couple of years ago, it took 3 weeks to prove 10^2100.
The goal of the run of july 2020 was to get the timing (it took 12 days) and to update the list of roadblocks.
Some composites would have been needed in order to circumvent sigma(3^660) or sigma(732541^46) but are not needed elsewhere.
They are not needed anymore and do not appear in the updated mwrb2100.txt

Since the program was not aiming at a new lower bound, it was run with trial factoring up to 300 only,
in order to catch the tiny factors that may cause the abundancy to exceed 2 (a higher trial limit or some ECM would slow things down).
This produces a load of uninteresting factors.
Trial factoring up to 10^10 is indeed required for roadblock composites. This is checked a posteriori.

The list of useful factors has been updated:
http://www.lirmm.fr/~ochem/opn/checkfacts.txt.gz
Quote:
 Does it even matter if there are unfound small factors in non-roadblock composites apart from them causing gcd errors?
No. The program encountered over 18 million composites, attacking them all with ECM would be a big effort for low benefit.
Most probably, the cofactor will be composite.
In this case, a given factor $$P$$ with $$d$$ digits counts for $$d$$ digits if $$P$$ is in the unfactored part
and counts for $$2d$$ digits if $$P$$ is in the factored part, because we can usually assume that $$P^2$$ divides the OPN.
So finding $$P$$ contributes only $$d$$ digits to the 2100 digits, in only one or few branches of the proof tree.

The composites worth considering are in mwrb2100.txt and t2100.txt

 2020-08-10, 17:55 #776 Brownfox     Dec 2017 2×29 Posts All of the remaining entries in the MWRB file have SNFS difficulty above 210. That is about the upper limit of my resources and NFSNET has reserved the next one, so this is a good point to stop working on this file.

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