[QUOTE=Mr. P-1;238415]Eventually, yes, but PRPs will do for now. Do you intend to do any more that 3-PRP on them?

I suppose I should parse his lists to find the first few 'status unknown' cofactors, to see if any are small enough to be PRP-tested.[/QUOTE]

I've tested them with bases =<7. 11 is done up to and including the cofactor of M86371 right now. And yes, all PRP so far.

I feel like this is too quick and easy to not have been done before... but maybe to few people care about extending factorizations.

[QUOTE=lorgix;238507]I feel like this is too quick and easy to not have been done before... but maybe to few people care about extending factorizations.[/QUOTE]

Eddington says they're all PRP to at least one base > 2. At this point, I think we can safely say they're all almost certainly prime.

[QUOTE=Mr. P-1;238515]Eddington says they're all PRP to at least one base > 2. At this point, I think we can safely say they're all almost certainly prime.[/QUOTE]

All 11-PRP too. OK.


There are two numbers with less than 2000digits.

M6199 has a 1813digit cofactor
M6337 has a 1802digit cofactor

I tested those two numbers with 10 other bases.

Anyone feel like proving those?

[QUOTE=lorgix;238357]The 1146digit factor of M4219 has been proved by factordb.[/QUOTE]

[url]http://www.mersenneforum.org/showpost.php?p=232133&postcount=6[/url]

[QUOTE=Mr. P-1;238591][URL]http://www.mersenneforum.org/showpost.php?p=232133&postcount=6[/URL][/QUOTE]

[URL]http://factorization.ath.cx/index.php?id=1100000000214492699[/URL]

I don't know which happened first.

[QUOTE=lorgix;238526]All 11-PRP too. OK.


There are two numbers with less than 2000digits.

M6199 has a 1813digit cofactor
M6337 has a 1802digit cofactor

I tested those two numbers with 10 other bases.

Anyone feel like proving those?[/QUOTE]

It seems an easy test with Primo...

E.T.

[QUOTE=ET_;238607]It seems an easy test with Primo...

E.T.[/QUOTE]

I was hoping someone would see it like that.

[CODE](2^6199-1)/179635392927728929353086482614805697378612611809363271
(2^6337-1)/4501318288109788011334762909785912975982707465271020857512756782053472363053668157533504357730278762590457[/CODE]Still no proof, afaik.

TO THE PRIMOBILE!!

[QUOTE=Mr. P-1;238257]I don't know whether database size is a problem. I imagine it's just that recording and coordination beyond the minimum necessary to find primes has been developed in a rather [I]ad hoc[/I] fashion.[/QUOTE]

The data I have is about 33 GB but some of that is simply historical rather than current. I've retained all output from my own runs, e.g., and all email sent to me related to Mersenne numbers.

[QUOTE=Mr. P-1;238257]I have a concrete example of what I've been talking about: M106391. This number has a 58 bit factor almost certainly discovered long ago by TF. The cofactor, according to [URL="http://www.garlic.com/%7Ewedgingt/factoredM.txt"]Eddington's list[/URL] "is at least a pseudo-prime in some base other than 2" according to his [URL="http://www.garlic.com/%7Ewedgingt/mersfmt.txt"]explanation of the codes[/URL]. Yet someone has done 15 curves on it.[/QUOTE]

I'm "Eddington" - Will Edgington, to correct the spelling (and I've only had half a dozen people get it right when they first hear it for some reason, so don't feel bad). I rarely have time to visit forums but thought I would take a look today after getting Oscar's email about M4871.

The 58 bit factor of M106391 is likely from GIMPS but I can find out for sure if someone wants to know; it should be in my files somewhere.

The ECM curves may have been done before the 58 bit factor was found.

That the cofactor is SPRP was almost certainly done by me with a program from the mers package that I maintain (see my web site, which I've added to my profile here). The current version of that program, sprpgmp, actually does 20 SPRP tests with random bases, so it is almost certainly SPRP to 20 distinct bases but may - if the random bases all happened to be identical - be SPRP for only one base. Perhaps I should modify the program to ensure the random bases are distinct.

[QUOTE=Mr. P-1;238257]Instead of ECM, further work on this exponent should focus on strengthening its probable prime status, (alternatively, proving that it is in fact composite, whereupon ECM could resume), in preparation for a future primality proof. At over 32,000 digits, a proof is probably unfeasible currently, but it may be reachable with a few years.[/QUOTE]

There are many much smaller SPRP cofactors to prove, including a few with less than 1200 digits for which the ECPP program I have has failed. Since I use Linux rather than MSWindows, most authors of such programs don't support my use of their programs.

Welcome to the forum, Will!

I'm just recently realizing how little interest there is in extending factorizations...

Would you be interested in sorting out the data so that we can start proving primes and identifying composites to factor? :smile:

[QUOTE=wedgingt;238686]I'm "Eddington" - Will Edgington, to correct the spelling (and I've only had half a dozen people get it right when they first hear it for some reason, so don't feel bad).[/QUOTE]

My apologies. In my defense I will say that I've lost my glasses and am using an older pair which is no longer fully up to the job.

[QUOTE=Mr. P-1;238257]Instead of ECM, further work on this exponent should focus on strengthening its probable prime status, (alternatively, proving that it is in fact composite, whereupon ECM could resume), in preparation for a future primality proof. At over 32,000 digits, a proof is probably unfeasible currently, but it may be reachable with a few years.[/QUOTE]

[QUOTE]There are many much smaller SPRP cofactors to prove, including a few with less than 1200 digits for which the ECPP program I have has failed.[/QUOTE]

I wasn't suggesting that work be done on it ahead of other tasks. My point was that further ECM should [i]not[/i] be done, and it should be removed from the PrimeNet's ECM progress list.

[QUOTE=Mr. P-1;238490]We are talking about all partially-factored prime-exponent Mersennes, not just the small ones. M8000053, for example, has a 27 bit factor, undoubtedly discovered long ago by TF. It's way too large for SNFS now or in the foreseeable future, but additional TF, P-1, or ECM might yeild more factors. Unfortunately, the database doesn't tell us how much TF beyond 27 bits or P-1, if any, has been done on this number. Nor does it tell us whether any primality or PRP tests have been done on the cofactor

You, personally, might not be interested in the discovery of additional factors short of complete factorisation. But other people are.[/QUOTE]

As an example of the additional data that I have, here is what I have for this exponent and some of its neighbors that have data. Note that not all of the exponents are prime. 'H' is highest trial factoring, 'c' is digits in the composite cofactor (by LL test when there's no known factor), 'o' is P-1 bounds, 'C' is a known factor, etc. The format is described on my web site and programs I've written can read and write it.

M( 8000023 )H: 18446744073709551616
M( 8000023 )c: 2408247
M( 8000023 )o: 40000 450000
M( 8000026 )C: 864002809
M( 8000027 )C: 13200044551
M( 8000028 )C: 32000113
M( 8000033 )C: 395137629937
M( 8000033 )C: 1906187238989927
M( 8000033 )H: 2252229690409151
M( 8000038 )C: 792003763
M( 8000039 )C: 16000079
M( 8000041 )C: 48000247
M( 8000044 )C: 96000529
M( 8000050 )C: 8000051
M( 8000051 )C: 208001327
M( 8000051 )H: 9223372036854775808
M( 8000053 )C: 128000849
M( 8000053 )H: 9223372036854775808
M( 8000054 )C: 7552050977
M( 8000055 )C: 400002751
M( 8000056 )C: 14576102033
M( 8000057 )C: 48000343
M( 8000063 )C: 4211141722479911
M( 8000063 )H: 4503696666331951