Seeking a proof that 5^7954+7954 is prime

Dougy · 2010-09-07, 01:01

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

CRGreathouse · 2010-09-07, 02:42

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).

schickel · 2010-09-07, 07:26

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.....

lavalamp · 2010-09-07, 11:29

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.

kar_bon · 2010-09-07, 11:55

See this thread with some useful hints from Cybertronic aka Norman Luhn (see posts 127 and 166).

Perhaps he can help out here!

Dougy · 2010-09-07, 12:22

Thanks for that, that's great! In either case, it would be significantly faster than if I ran it myself.

lavalamp · 2010-09-07, 13:19

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.

schickel · 2010-09-08, 07:54

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.

lavalamp · 2010-09-08, 08:41

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.

schickel · 2010-09-08, 09:18

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.

lavalamp · 2010-09-08, 09:37

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.

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

2010-09-08, 08:41	#9
lavalamp Oct 2007 Manchester, UK 2×3×223 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

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2010-09-07, 02:42	#2
CRGreathouse Aug 2006 3×1,987 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, 11:29	#4
lavalamp Oct 2007 Manchester, UK 2·3·223 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 2×1,433 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 230₈ 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 2×3×223 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.