[QUOTE=science_man_88;467595]to be fair other than primes the cofactor can't divisors up to a 106 digit number otherwise the composite divisor would have to divide by one of the primes already given or a prime below the last divisor shown.[/QUOTE]

How do you figure? I failed to parse your run-on. Also, you mean 106 bits, rather than digits, amirite? What does "other than primes the cofactor can't divisors" mean? The cofactor can't have divisors other than primes? eh?

Mostly I'd like to know where you got 106 digits, but a translation of the rest would be appreciated.

[QUOTE=GP2;467569]No, but these exponents are a tad larger than the Cunningham project limit.[/QUOTE]Nonetheless, I know Sam collects factors larger than the official limits (I once sent him some Aur. base-3 factors which he later used in an extension to that table) and I also know he keeps in contact with others who factor such things.

[QUOTE=science_man_88;467595]to be fair other than primes the cofactor can't divisors up to a 106 digit number otherwise the composite divisor would have to divide by one of the primes already given or a prime below the last divisor shown.[/QUOTE]I can't parse that. What?

the highest known factor right now, is about 53 digits. Any composite below it's square (106 digits, according to PARI/GP.) , would have to contain an earlier factor, if the factors up to that point are complete. so it's only primes up to the 106 digits of that square that can divide ( and assuming the factorization is complete up until that factor, above that factor as well).

[QUOTE=GP2;467589]...So, if anything, the mystery person might be trying to find "last factors" rather than first factors.
Also, anyone that contributes to these forums would surely manually report any new finds to PrimeNet, which our mystery person is not doing.[/QUOTE]
Since about August 3, 2017, factors of 2^n-1 have been added to FactorDB for most or all of n \in 1501, 1529, 1529, 1563, 1563, 1507, 1497, 1591, 1457, 1595, 1629, 1687, 1711, 1859, 1959, 1963, 1445, 1479, 1491, 1467, 1465, 1441, 1489, 1595, 1471, 1445, and 1525. Only two of those have prime "n". I downloaded some factors from jcrombie's factors.zip file into my own tiny database, and then uploaded some of my new factors to factordb. (I don't have a good record, but I see something around a half dozen to a dozen where the timestamp of the factorization in my database is earlier than the timestamp in factordb, and that doesn't include either of the Mersenne numbers.) It seems as though one or more other people are working on near-Cunningham numbers. Maybe the two Mersenne numbers were just a coincidence. ryanp acknowledges factoring a couple of these in the ElevenSmooth thread.

[QUOTE=GP2;467589]OK, except these are not exponents with no known factors. In fact, M[M]1471[/M] is now fully factored and M[M]1489[/M] is now 34% factored and the remaining composite cofactor is well within range of NFS. So, if anything, the mystery person might be trying to find "last factors" rather than first factors.

Also, anyone that contributes to these forums would surely manually report any new finds to PrimeNet, which our mystery person is not doing.[/QUOTE]
The clue I referred to in my post, was to the identity of the user kkmrkkblmbrbk

[QUOTE=science_man_88;467621]the highest known factor right now, is about 53 digits. Any composite below it's square (106 digits, according to PARI/GP.) , would have to contain an earlier factor, if the factors up to that point are complete. so it's only primes up to the 106 digits of that square that can divide ( and assuming the factorization is complete up until that factor, above that factor as well).[/QUOTE]
"If we know all factors below n digits, then any factor smaller than 2n-1 digits that we find next must be prime."

1. How is this helpful in any way?
2. Do you have even the slightest grasp of ECM to realize that finding a factor of, say, 53 digits does *nothing* to tell you there aren't any factors below 53 digits?

If you mean to suggest that we wouldn't need to test primality on a factor if it's smaller than 106 digits, perhaps you should also discover how long a primality test is on a 90-digit number, versus what work it would take to be sure there were no factors below 53 digits. Your observation, while utterly trivially true, allows someone to spend years of trial factoring to save milliseconds of a primality test.

[QUOTE=Dr Sardonicus;467635]The clue I referred to in my post, was to the identity of the user kkmrkkblmbrbk[/QUOTE]

Yeah, that guy, he's a real weirdo. But he's not the discoverer of those factors, he just manually reported them to PrimeNet. The actual discoverer, whoever that is, only reported them to FactorDB.

[QUOTE=Dr Sardonicus;467635]The clue I referred to in my post, was to the identity of the user kkmrkkblmbrbk[/QUOTE]

That is GP2's primenet id. He got the factor from factordb and reported it to mersenne.org.

EDIT:- Cross-posted with GP2.

[QUOTE=GP2;467638]Yeah, that guy, he's a real weirdo. But he's not the discoverer of those factors, he just manually reported them to PrimeNet. The actual discoverer, whoever that is, only reported them to FactorDB.[/QUOTE]So much for my vaunted skills at tracking things down or looking them up
:blush:

I'll see if I can do better...

[QUOTE=swellman;467939]That's the work of Ryan Propper. He's got most or all of the composite cofactors of M(3326400) < 1000 digits undergoing ECM. He's found a couple of factors in the big fdb list, as well as a couple from the list on the ElevenSmooth project page. Anything found from the list on the 11S page is reported here.

Ryan is also attempting the lowest difficulty SNFS composites as well, with factors reported here. There do not appear to be many feasible SNFS factorization jobs left in that project.[/QUOTE]

Is this possibly the mysterious contributor who's added these factors to FDB? I've only barely skimmed both threads in question, but I believe this might be the culprit this thread is looking for.

Edit: Nevermind, that was about composite Mersennes, which as far as I can tell have only small prime factors -- not the large-ish primes above 1000 as are in question here.