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 2018-10-12, 15:47 #430 VBCurtis     "Curtis" Feb 2005 Riverside, CA 10DD16 Posts May I reserve the Primo run to verify primality of the M51487 cofactor?
2018-10-12, 16:44   #431
GP2

Sep 2003

258010 Posts

Quote:
 Originally Posted by VBCurtis May I reserve the Primo run to verify primality of the M51487 cofactor?
I think you just did, unless anyone objects.

2018-10-12, 16:58   #432
axn

Jun 2003

2×2,347 Posts

Quote:
 Originally Posted by VBCurtis 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

2018-10-12, 17:54   #433
GP2

Sep 2003

A1416 Posts

Quote:
 Originally Posted by axn Should easily make it into https://primes.utm.edu/top20/page.php?id=49
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.

2018-10-12, 19:06   #434
paulunderwood

Sep 2002
Database er0rr

23×52×17 Posts

Quote:
 Originally Posted by GP2 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.

2018-10-12, 20:29   #435
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100011101001102 Posts

Quote:
 Originally Posted by GP2 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.

2018-10-13, 16:38   #436
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

3×1,439 Posts

Quote:
 Originally Posted by VBCurtis 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.

2018-10-13, 17:06   #437
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100011101001102 Posts

Quote:
 Originally Posted by VBCurtis ... unreserving this cofactor.
Reserving M51487 cofactor. Should be a few weeks to a month.

 2018-10-13, 17:38 #438 GP2     Sep 2003 1010000101002 Posts 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?
 2018-10-23, 14:18 #439 alpertron     Aug 2002 Buenos Aires, Argentina 33·72 Posts 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.
2018-11-05, 02:38   #440
paulunderwood

Sep 2002
Database er0rr

340010 Posts

Quote:
 Originally Posted by Batalov 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

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