mersenneforum.org Want to test a known prime number manually.
 Register FAQ Search Today's Posts Mark Forums Read

 2020-05-18, 17:04 #1 LOBES   Mar 2019 38 Posts Want to test a known prime number manually. I recently found the 2641st largest prime known to mankind (fame to come I'm sure) using the Genefer 16 sub-project at PrimeGrid. The number is 93043462^65536 + 1 Because I simply enjoy it, I would like to test this number manually using Prime95 but I'm not exactly sure how I would format the entry in worktodo.txt? What would be the proper syntax for testing this number, if of course, its even possible?
2020-05-18, 17:40   #2
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

2×32×227 Posts

Quote:
 Originally Posted by LOBES I recently found the 2641st largest prime known to mankind (fame to come I'm sure) using the Genefer 16 sub-project at PrimeGrid. The number is 93043462^65536 + 1 Because I simply enjoy it, I would like to test this number manually using Prime95 but I'm not exactly sure how I would format the entry in worktodo.txt? What would be the proper syntax for testing this number, if of course, its even possible?
A direct quote from the prime95 readme.txt file:
Code:
The PRP choice, available from the menus only in the Mac OS X version, lets you do a
probable prime test on numbers of the form k*b^n+c.  On all OSes, you can edit
the worktodo.txt file directly.  For example add:
PRP=k,b,n,c[,how_far_factored,tests_saved][,prp_base,residue_type][,"comma-separated-list-of-known-factors"]
where the how_far_factored and tests_saved values are used to pick
optimal bounds for P-1 factoring prior to running the PRP test.
Should not take long to run compared to current GIMPS work.
PRP=N/A,1,93043462,65536,1,86,2 inserted into the worktodo.txt file and run, indicates ~73 minutes on my Win10 i7-8750H in the worker window, with a 192K fft length, but oddly about 10 years estimate in the status option. I'm inclined to believe the worker.
For GIMPS worktodo formats in general, see https://www.mersenneforum.org/showpo...8&postcount=22

edit: as Batalov reminds in the next post, PRP does not prove it prime; it can show something composite but can't prove it prime. It at best indicates probably prime with a high probability.
Attached Thumbnails

Last fiddled with by kriesel on 2020-05-18 at 17:56

 2020-05-18, 17:41 #3 Batalov     "Serge" Mar 2008 Phi(3,3^1118781+1)/3 906210 Posts Welcome, Greg! The primality of this number can be tested with other tools, pfgw or maybe llr. observe the webpage - https://primes.utm.edu/primes/page.php?id=130905 and scroll to the lower part (Ctrl-F pfgw); this command line can be replicated on your computer. And if you really like Prime95, yes, you can test this number for probable-primality (so called PRP test; also note that this also what GeneFer GPU program did, - a PRP test), but after that you still need to test it for strict primality.
 2020-05-19, 06:17 #4 kuratkull     Mar 2007 Estonia 2·67 Posts I can appreciate strict primality over PRP of course. But I would like to point out that the likelihood PRPs the size of this specific number being Fermat liars is in the neighborhood of 10-50000. So there's no real doubt large PRP's are prime, it's mostly a technical difference. Source: https://primes.utm.edu/notes/prp_prob.html Last fiddled with by kuratkull on 2020-05-19 at 06:21
2020-05-19, 08:15   #5
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

3·1,847 Posts

Quote:
 Originally Posted by kuratkull I can appreciate strict primality over PRP of course. But I would like to point out that the likelihood PRPs the size of this specific number being Fermat liars is in the neighborhood of 10-50000. So there's no real doubt large PRP's are prime, it's mostly a technical difference. Source: https://primes.utm.edu/notes/prp_prob.html
Beyond reasonable doubt. Indeed.

But mathematicians aren't reasonable minded when it comes to proofs. There is no room for doubt.

 Similar Threads Thread Thread Starter Forum Replies Last Post bosons Factoring 29 2019-11-12 13:58 king Information & Answers 5 2018-02-21 18:15 king Information & Answers 6 2018-02-08 14:28 mohdosa Information & Answers 22 2014-10-10 11:34 laich2 PrimeNet 6 2012-01-16 04:51

All times are UTC. The time now is 10:33.

Tue Jul 14 10:33:23 UTC 2020 up 111 days, 8:06, 0 users, load averages: 1.55, 1.46, 1.41