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-   -   Mersenne number factored (disbelievers are biting elbows) (https://www.mersenneforum.org/showthread.php?t=19407)

 VBCurtis 2018-10-12 15:47

May I reserve the Primo run to verify primality of the M51487 cofactor?

 GP2 2018-10-12 16:44

[QUOTE=VBCurtis;497940]May I reserve the Primo run to verify primality of the M51487 cofactor?[/QUOTE]

I think you just did, unless anyone objects.

 axn 2018-10-12 16:58

[QUOTE=VBCurtis;497940]May I reserve the Primo run to verify primality of the M51487 cofactor?[/QUOTE]

Should easily make it into [url]https://primes.utm.edu/top20/page.php?id=49[/url]

 GP2 2018-10-12 17:54

[QUOTE=axn;497947]Should easily make it into [url]https://primes.utm.edu/top20/page.php?id=49[/url][/QUOTE]

Mersenne numbers are the b=2 special cases of generalized repunits (b[SUP]p[/SUP] − 1) / (b − 1).

I compared Chris Caldwell's [URL="https://primes.utm.edu/top20/page.php?id=49"]list of Mersenne PRP cofactors[/URL], where the largest is not quite 20,000 digits, and his [URL="https://primes.utm.edu/top20/page.php?id=16"]list of generalized repunit PRPs[/URL], 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 (b[SUP]p[/SUP] − 1) divided by some divisor? And perhaps easier to find PRPs in the first place?

However, looking at the [URL="http://www.primenumbers.net/prptop/prptop.php"]Lifchitz list of top PRPs[/URL], 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.

 paulunderwood 2018-10-12 19:06

[QUOTE=GP2;497953]Mersenne numbers are the b=2 special cases of generalized repunits (b[SUP]p[/SUP] − 1) / (b − 1).

I compared Chris Caldwell's [URL="https://primes.utm.edu/top20/page.php?id=49"]list of Mersenne PRP cofactors[/URL], where the largest is not quite 20,000 digits, and his [URL="https://primes.utm.edu/top20/page.php?id=16"]list of generalized repunit PRPs[/URL], 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 (b[SUP]p[/SUP] − 1) divided by some divisor? And perhaps easier to find PRPs in the first place?

However, looking at the [URL="http://www.primenumbers.net/prptop/prptop.php"]Lifchitz list of top PRPs[/URL], 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.[/QUOTE]

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.

 Batalov 2018-10-12 20:29

[QUOTE=GP2;497953]Is it somehow generally true that for larger b it is easier to prove primality of (b[SUP]p[/SUP] − 1) divided by [STRIKE]some[/STRIKE] algebraic divisor? [/QUOTE]
(b[SUP]p[/SUP] − 1) / (b − 1) - 1 = x * (b[SUP]p-1[/SUP] − 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 [url]https://primes.utm.edu/top20/page.php?id=16[/url], are enriched with harder proof methods but if you use [url]https://primes.utm.edu/primes/search.php[/url], 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.

 VBCurtis 2018-10-13 16:38

[QUOTE=VBCurtis;497940]May I reserve the Primo run to verify primality of the M51487 cofactor?[/QUOTE]

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.

 Batalov 2018-10-13 17:06

[QUOTE=VBCurtis;497996]... unreserving this cofactor.[/QUOTE]
Reserving M51487 cofactor. Should be a few weeks to a month.

 GP2 2018-10-13 17:38

Has anyone tried the [c]primecert[/c] and [c]primecertexport[/c] 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?

 alpertron 2018-10-23 14:18

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 [FONT="Courier New"]sudo apt-get update[/FONT]
4) Type [FONT="Courier New"]sudo apt-get upgrade[/FONT]
5) Type [FONT="Courier New"]sudo apt-get install gdk-pixbuf2.0-0[/FONT]
6) Type [FONT="Courier New"]sudo apt-get install libgtk2.0-dev[/FONT]
7) Type [FONT="Courier New"]sudo apt-get install xdg-utils[/FONT]
8) Open .bashrc (I used nano), add the following line at the end of this file:
[FONT="Courier New"]export DISPLAY=:0[/FONT] and save it.
10) Close Bash for Windows
11) Ensure that Xming is running
12) Open Bash for Windows
13) Run Primo and enjoy.

 paulunderwood 2018-11-05 02:38

[QUOTE=Batalov;498000]Reserving M51487 cofactor. Should be a few weeks to a month.[/QUOTE]

Congrats for the proof. [url]https://primes.utm.edu/primes/page.php?id=125757[/url]

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