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 2010-09-07, 01:01 #1 Dougy     Aug 2004 Melbourne, Australia 23×19 Posts Seeking a proof that 5^7954+7954 is prime Hi guys, Could someone please prove that 5^7954+7954 is prime? This question came up on math.stackexchange.com (here is the question). I won't be able to run Primo for long enough due to travelling. - Dougy
 2010-09-07, 02:42 #2 CRGreathouse     Aug 2006 32×5×7×19 Posts It's a BPSW probable prime, and a strong pseudoprime to 100 randomly-selected bases. I don't have the resources to prove it at the moment, but it's almost surely prime (even if selected by an adversary).
2010-09-07, 07:26   #3
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2×1,061 Posts

Quote:
 Originally Posted by Dougy Hi guys, Could someone please prove that 5^7954+7954 is prime? This question came up on math.stackexchange.com (here is the question). I won't be able to run Primo for long enough due to travelling. - Dougy
If no one offers something bigger, I've got a spare system I could run it on; it won't be fast though, it's only a 3 GHz Pentium D.....

 2010-09-07, 11:29 #4 lavalamp     Oct 2007 Manchester, UK 17×79 Posts I've started it on a core of a 2.4 GHz Core 2 Duo PC, shame Primo isn't multi-threaded. I guesstimate around 37 days runtime based on info here: http://mathworld.wolfram.com/Ellipti...tyProving.html Through simple clock speed scaling, I guesstimate 30 days running on your 3 GHz Pentium D. I suppose it does somewhat depend on how Primo has been updated and optimised to run on the Core architecture. Does anyone have any better estimates? The number is 5560 digits or 18469 bits in length.
 2010-09-07, 11:55 #5 kar_bon     Mar 2006 Germany 55018 Posts See this thread with some useful hints from Cybertronic aka Norman Luhn (see posts 127 and 166). Perhaps he can help out here!
 2010-09-07, 12:22 #6 Dougy     Aug 2004 Melbourne, Australia 23·19 Posts Thanks for that, that's great! In either case, it would be significantly faster than if I ran it myself.
 2010-09-07, 13:19 #7 lavalamp     Oct 2007 Manchester, UK 17·79 Posts kar_bon, I think I managed to make some sense of post 127, using a pair of translators to compensate for each others deficiencies. However, I don't think I'll bother hacking into the intermediate files of Primo as I don't understand anywhere near enough about it for that. I'd almost certainly end up wasting weeks of CPU time computing nonsense.
2010-09-08, 07:54   #8
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2·1,061 Posts

Quote:
 Originally Posted by lavalamp Through simple clock speed scaling, I guesstimate 30 days running on your 3 GHz Pentium D.
I hadn't estimated yet, but I knew it was going to be slow after it didn't advance any bits after seven hours...I would have had to kick one of my sieve jobs off a faster core to make any progress.

 2010-09-08, 08:41 #9 lavalamp     Oct 2007 Manchester, UK 24778 Posts Here's where mine is after nearly a day of running. Edit: I should point out that I have basically no idea what any of the status info means. Attached Thumbnails   Last fiddled with by lavalamp on 2010-09-08 at 08:45
2010-09-08, 09:18   #10
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2·1,061 Posts

Quote:
 Originally Posted by lavalamp Here's where mine is after nearly a day of running. Edit: I should point out that I have basically no idea what any of the status info means.
From running a couple of proofs a while back (3 years? time files....), the thing to watch is the "bits" field. The number under test is 18469 bits long; as the "numerator" decreases, that means that Primo is working on the proof for the smaller number. It starts *very* slowly, with the speed increasing as the numbers get smaller.

Two things: if you want to use the PC at all, check the "Idle" box, otherwise Primo will monopolize the CPU; and check the "Double file management" box if you don't have a UPS, that way Primo will keep backups of the temp files as it works, just in case the power were to quit while it was writing a file.

2010-09-08, 09:37   #11
lavalamp

Oct 2007
Manchester, UK

17·79 Posts

Quote:
 Originally Posted by schickel Two things: if you want to use the PC at all, check the "Idle" box, otherwise Primo will monopolize the CPU; and check the "Double file management" box if you don't have a UPS, that way Primo will keep backups of the temp files as it works, just in case the power were to quit while it was writing a file.
Sadly I can't check the double file management box now that it's already running. I don't really want to stop it in case I can't start it again. Power cuts here are very rare, so lets hope there isn't one in the next month or so while it's writing out a file.

As far as the idle box, I deliberately unchecked that one so that it can pretty much have the core all to itself and not have to give way. It's a dual core machine and nothing else it does will max out the other core.

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