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LOBES 2020-05-18 17:04

Want to test a known prime number manually.
 
I recently found the 2641[SUP]st[/SUP] largest prime known to mankind (fame to come I'm sure) using the Genefer 16 sub-project at PrimeGrid. The number is 93043462^[SUP]65536[/SUP] + 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?

kriesel 2020-05-18 17:40

1 Attachment(s)
[QUOTE=LOBES;545741]I recently found the 2641[SUP]st[/SUP] largest prime known to mankind (fame to come I'm sure) using the Genefer 16 sub-project at PrimeGrid. The number is 93043462^[SUP]65536[/SUP] + 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?[/QUOTE]
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.[/CODE]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 [URL]https://www.mersenneforum.org/showpost.php?p=522098&postcount=22[/URL]


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.

Batalov 2020-05-18 17:41

Welcome, Greg!

The primality of this number can be tested with other tools, pfgw or maybe llr.
observe the webpage - [url]https://primes.utm.edu/primes/page.php?id=130905[/url] 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.

kuratkull 2020-05-19 06:17

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[SUP]-50000[/SUP]. So there's no real doubt large PRP's are prime, it's mostly a technical difference.
Source: [URL]https://primes.utm.edu/notes/prp_prob.html[/URL]

retina 2020-05-19 08:15

[QUOTE=kuratkull;545826]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[SUP]-50000[/SUP]. So there's no real doubt large PRP's are prime, it's mostly a technical difference.
Source: [URL]https://primes.utm.edu/notes/prp_prob.html[/URL][/QUOTE]Beyond reasonable doubt. Indeed.

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


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