mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > PrimeNet

Reply
 
Thread Tools
Old 2017-02-07, 01:34   #1
mattmill30
 
Aug 2015

2·23 Posts
Default Fully factored

Is there a "fully TF'd" list of exponents on mersenne.ca?
mattmill30 is offline   Reply With Quote
Old 2017-02-07, 04:54   #2
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

2·3·7·113 Posts
Default

Define "fully TF'ed". Do you mean fully factored?
VBCurtis is offline   Reply With Quote
Old 2017-02-07, 18:57   #3
mattmill30
 
Aug 2015

568 Posts
Default

Yes, fully factored
mattmill30 is offline   Reply With Quote
Old 2017-02-07, 19:21   #4
Siegmund
 
Siegmund's Avatar
 
Mar 2014

4810 Posts
Default

This would be an interesting list to see.

I suspect there are very few large exponents on the list -- finding one 60- or 70-bit factor of a million-digit number leaves a very large nut to crack.
Siegmund is offline   Reply With Quote
Old 2017-02-07, 20:44   #5
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

2·3·7·113 Posts
Default

Check the top-5000 primes page for mersenne cofactors.
I assume there is a prp version of that page too with larger cofactors too big for ECPP just yet- perhaps someone could aim me the right direction?
VBCurtis is offline   Reply With Quote
Old 2017-02-07, 21:17   #6
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×37×127 Posts
Default

A superset of the PRPs is here.

There are some (2ap-1)/(2a-1)/f as you can see.
If you replace "?" with "f", then you could miss some cofactors that were submitted like (2p-1)/f1/f2
Batalov is offline   Reply With Quote
Old 2017-02-07, 21:25   #7
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

2·72·37 Posts
Default

Yes: top 20 Mersenne cofactors (proven).

There are some outstanding ones less than Primo's 35k digit limit.

Here the reported gigantic PRPs -- I dare say Henri's list is out of date, in that some PRPs are proven primes.

I am currently proving a ~15k digit Mersenne cofactor -- ETA less than a month form now.
paulunderwood is offline   Reply With Quote
Old 2017-02-08, 04:02   #8
GP2
 
GP2's Avatar
 
Sep 2003

22·647 Posts
Default

Quote:
Originally Posted by paulunderwood View Post
Here the reported gigantic PRPs -- I dare say Henri's list is out of date, in that some PRPs are proven primes.
It also has the problem that the formats of the entries are not normalized, but are simply stored however they were reported. For example M1790743 does not appear in the link you gave because it is stored as (2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) and therefore doesn't match the pattern (2^p-1)/n

Similarly M4834891, M822971, M750151, M696343, M675977, M576551, M488441, M440399, M270059, M157457, M41681 are missing. All of these do appear when you click the "The Full PRP Top" (on the first page from 1 to 250, or subsequent pages).
GP2 is offline   Reply With Quote
Old 2017-02-08, 04:08   #9
GP2
 
GP2's Avatar
 
Sep 2003

22×647 Posts
Default

Quote:
Originally Posted by mattmill30 View Post
Is there a "fully TF'd" list of exponents on mersenne.ca?
Yes, here is the complete list. There are currently 310 fully-factored or probably-fully-factored exponents, in addition to the Mersenne primes themselves which are certainly also fully factored.

Only 63703 and smaller are certified and proven to be fully factored, the higher exponents have a probable-prime (PRP) cofactor, albeit with extremely high confidence.

Last fiddled with by GP2 on 2017-02-08 at 04:12
GP2 is offline   Reply With Quote
Old 2017-02-08, 17:35   #10
Xyzzy
 
Xyzzy's Avatar
 
"Mike"
Aug 2002

1F7C16 Posts
Default

Quote:
Originally Posted by GP2 View Post
Yes, here is the complete list. There are currently 310 fully-factored or probably-fully-factored exponents, in addition to the Mersenne primes themselves which are certainly also fully factored.

Only 63703 and smaller are certified and proven to be fully factored, the higher exponents have a probable-prime (PRP) cofactor, albeit with extremely high confidence.
A lot of those PRP cofactors could be tested easily. We wonder why nobody has done that.

Xyzzy is offline   Reply With Quote
Old 2017-02-08, 18:30   #11
GP2
 
GP2's Avatar
 
Sep 2003

22×647 Posts
Default

Quote:
Originally Posted by Xyzzy View Post
A lot of those PRP cofactors could be tested easily. We wonder why nobody has done that.
I imagine it's harder than you think.

The record for Primo is 34093 decimal digits, which took 14 months with 48 cores, plus 200 additional days with 6 cores, by none other than Paul Underwood.

Based on that, M106391 (with a cofactor of 32010 decimal digits) is the largest Mersenne exponent that could feasibly be fully factored at the present time. The next smallest is M130439, with a cofactor of 39261 decimal digits.

Last fiddled with by GP2 on 2017-02-08 at 18:32
GP2 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Largest Mersenne Number Fully Factored? c10ck3r Data 49 2017-12-10 19:39
Exponent fully factored whilst only 74% known mattmill30 Factoring 3 2016-08-14 18:09
Possibility of a Fully-Factored Number Trejack FactorDB 7 2016-05-14 05:38
Factored vs. Completely factored aketilander Factoring 4 2012-08-08 18:09
New program to fully factor with GMP-ECM rogue GMP-ECM 51 2009-06-01 12:53

All times are UTC. The time now is 10:32.

Thu Apr 22 10:32:05 UTC 2021 up 14 days, 5:12, 0 users, load averages: 2.64, 2.20, 1.92

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.