mersenneforum.org  

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

Reply
 
Thread Tools
Old 2018-10-12, 15:47   #430
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

10DD16 Posts
Default

May I reserve the Primo run to verify primality of the M51487 cofactor?
VBCurtis is offline   Reply With Quote
Old 2018-10-12, 16:44   #431
GP2
 
GP2's Avatar
 
Sep 2003

258010 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
May I reserve the Primo run to verify primality of the M51487 cofactor?
I think you just did, unless anyone objects.
GP2 is offline   Reply With Quote
Old 2018-10-12, 16:58   #432
axn
 
axn's Avatar
 
Jun 2003

2×2,347 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
May I reserve the Primo run to verify primality of the M51487 cofactor?
Should easily make it into https://primes.utm.edu/top20/page.php?id=49
axn is offline   Reply With Quote
Old 2018-10-12, 17:54   #433
GP2
 
GP2's Avatar
 
Sep 2003

A1416 Posts
Default

Quote:
Originally Posted by axn View Post
Mersenne numbers are the b=2 special cases of generalized repunits (bp − 1) / (b − 1).

I compared Chris Caldwell's list of Mersenne PRP cofactors, where the largest is not quite 20,000 digits, and his list of generalized repunit PRPs, where the digit lengths go up to 95,000 digits.

The generalized repunit PRPs in the list all have large b, in the thousands or tens of thousands. Nearly all of the primality certificates are by Tom Wu.

Is it somehow generally true that for larger b it is easier to prove primality of (bp − 1) divided by some divisor? And perhaps easier to find PRPs in the first place?

However, looking at the Lifchitz list of top PRPs, however, the top 1 and 2 are Wagstaff (repunit with b=−2), numbers 4, 5, 6, 8 and 14 are Mersenne cofactors (repunit with b=2), number 11 is a repunit PRP with b=−13, number 12 is a repunit PRP with b=5, etc. I don't see any large b bases in the top rankings.
GP2 is offline   Reply With Quote
Old 2018-10-12, 19:06   #434
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

23×52×17 Posts
Default

Quote:
Originally Posted by GP2 View Post
Mersenne numbers are the b=2 special cases of generalized repunits (bp − 1) / (b − 1).

I compared Chris Caldwell's list of Mersenne PRP cofactors, where the largest is not quite 20,000 digits, and his list of generalized repunit PRPs, where the digit lengths go up to 95,000 digits.

The generalized repunit PRPs in the list all have large b, in the thousands or tens of thousands. Nearly all of the primality certificates are by Tom Wu.

Is it somehow generally true that for larger b it is easier to prove primality of (bp − 1) divided by some divisor? And perhaps easier to find PRPs in the first place?

However, looking at the Lifchitz list of top PRPs, however, the top 1 and 2 are Wagstaff (repunit with b=−2), numbers 4, 5, 6, 8 and 14 are Mersenne cofactors (repunit with b=2), number 11 is a repunit PRP with b=−13, number 12 is a repunit PRP with b=5, etc. I don't see any large b bases in the top rankings.
The big proven GRUs are done with CHG or KP proof methods where a great deal of finding and proving the factors of N^2-1 is done, whereas the Mersenne cofactors are purely ECPP.
paulunderwood is online now   Reply With Quote
Old 2018-10-12, 20:29   #435
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100011101001102 Posts
Default

Quote:
Originally Posted by GP2 View Post
Is it somehow generally true that for larger b it is easier to prove primality of (bp − 1) divided by some algebraic divisor?
(bp − 1) / (b − 1) - 1 = x * (bp-1 − 1),
so if p-1 is fairly smooth, and some of the cofactors happen to be prime, then you have a path to N-1 proof. Same for N+1.
What we see at the top https://primes.utm.edu/top20/page.php?id=16, are enriched with harder proof methods but if you use https://primes.utm.edu/primes/search.php, and search for Text Comment = Generalized Repunit, Type = all, Maximum number of primes to output = 2000, you will find tons of simple N+-1 proofs, as well.
Batalov is offline   Reply With Quote
Old 2018-10-13, 16:38   #436
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

3×1,439 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
May I reserve the Primo run to verify primality of the M51487 cofactor?
It has been a while since I've used Primo; I forgot that it lacks command-line interface, and I have only SSH access to my 40-thread workstation. I should put some time into re-learning Primo usage on smaller inputs before I tackle a multi-month job; unreserving this cofactor.
VBCurtis is offline   Reply With Quote
Old 2018-10-13, 17:06   #437
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100011101001102 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
... unreserving this cofactor.
Reserving M51487 cofactor. Should be a few weeks to a month.
Batalov is offline   Reply With Quote
Old 2018-10-13, 17:38   #438
GP2
 
GP2's Avatar
 
Sep 2003

1010000101002 Posts
Default

Has anyone tried the primecert and primecertexport functions in recent PARI/GP versions? The documentation says it can create a Primo v. 4 certificate. How does the speed compare with the actual Primo program?
GP2 is offline   Reply With Quote
Old 2018-10-23, 14:18   #439
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

33·72 Posts
Default

I was able to configure Bash for Windows to run Primo on Windows 10.

I performed the following steps in Ubuntu 18.04 on Bash for Windows:

1) Install Xming (the X server)
2) Open Bash for Windows
3) Type sudo apt-get update
4) Type sudo apt-get upgrade
5) Type sudo apt-get install gdk-pixbuf2.0-0
6) Type sudo apt-get install libgtk2.0-dev
7) Type sudo apt-get install xdg-utils
8) Open .bashrc (I used nano), add the following line at the end of this file:
export DISPLAY=:0 and save it.
9) Download the latest version of Primo and decompress it in a directory that can be seen on Bash for Windows
10) Close Bash for Windows
11) Ensure that Xming is running
12) Open Bash for Windows
13) Run Primo and enjoy.
alpertron is offline   Reply With Quote
Old 2018-11-05, 02:38   #440
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

340010 Posts
Default

Quote:
Originally Posted by Batalov View Post
Reserving M51487 cofactor. Should be a few weeks to a month.
Congrats for the proof. https://primes.utm.edu/primes/page.php?id=125757

Last fiddled with by paulunderwood on 2018-11-05 at 02:39
paulunderwood is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Smallest exponent for mersenne not-factored preda PrimeNet 10 2018-11-04 00:47
Largest Mersenne Number Fully Factored? c10ck3r Data 49 2017-12-10 19:39
Possibility of a Fully-Factored Number Trejack FactorDB 7 2016-05-14 05:38
Estimating the number of primes in a partially-factored number CRGreathouse Probability & Probabilistic Number Theory 15 2014-08-13 18:46
Number of distinct prime factors of a Double Mersenne number aketilander Operazione Doppi Mersennes 1 2012-11-09 21:16

All times are UTC. The time now is 23:10.

Wed Sep 23 23:10:26 UTC 2020 up 13 days, 20:21, 0 users, load averages: 1.59, 1.66, 1.66

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, 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.