20200518, 17:04  #1 
Mar 2019
3_{10} Posts 
Want to test a known prime number manually.
I recently found the 2641^{st} largest prime known to mankind (fame to come I'm sure) using the Genefer 16 subproject 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? 
20200518, 17:40  #2  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2×43×47 Posts 
Quote:
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][,"commaseparatedlistofknownfactors"] where the how_far_factored and tests_saved values are used to pick optimal bounds for P1 factoring prior to running the PRP test. PRP=N/A,1,93043462,65536,1,86,2 inserted into the worktodo.txt file and run, indicates ~73 minutes on my Win10 i78750H 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. Last fiddled with by kriesel on 20200518 at 17:56 

20200518, 17:41  #3 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
5·1,811 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 (CtrlF pfgw); this command line can be replicated on your computer. And if you really like Prime95, yes, you can test this number for probableprimality (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. 
20200519, 06:17  #4 
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 20200519 at 06:21 
20200519, 08:15  #5  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5530_{10} Posts 
Quote:
But mathematicians aren't reasonable minded when it comes to proofs. There is no room for doubt. 

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