2^9092392+40291 is a probable prime! - Page 2

enderak · 2011-02-09, 22:16

As expected, my double-check came back matching!

Quote:

2^9092392+40291 is a probable prime! We4: 16576B3B,00000000

paulunderwood · 2011-02-09, 22:28

Quote:

Originally Posted by enderak

As expected, my double-check came back matching!

A very nice find. Congratulations to all those involved. It is by far the largest PRP found to date. If it were proven prime it would rank 13th largest prime, but as it can not be (in a reasonable amount of time) it tops Henri Lifchitz's PRP database along with Five or Bust's other two Mega PRPs.

Batalov · 2011-02-09, 22:56

Quote:

Originally Posted by enderak

As expected, my double-check came back matching!

[pedantic]Re: the thread title. Capt.Obvious reports that We1 (Wd4, etc) values (i.e. "We1: 16576B3B") are workunit hashes; these values will match (they are a hash of the input, not the output) -- regardless of the test result (which in this case of course did match, too; it was a 0 in all bits). [/pedantic]
Anyway,

MooMoo2 · 2011-02-09, 22:57

Congrats! Just out of curiosity, will this forum be placed in the "Archived projects" section when all doublechecks are complete?

Mini-Geek · 2011-02-10, 00:38

Congratulations on (probably

) proving the conjecture this project set out to prove! Next step is to wait for incredibly fast computers, or maybe quantum computer factoring for N-1/N+1, or maybe a new primality proving algorithm that makes ECPP look slow, and you can actually prove that these PRPs are all prime and that the conjecture is proven.

Well, you can always keep edging up the lower end of proving the PRPs up slowly in the mean time.

paleseptember · 2011-02-10, 00:55

Fantastic work! I come back from holidays to find that the project has (almost certainly) been wrapped up!
My workunits have finished (no PRPs, no ninja'ing), and have just been emailed off to Phil. I had some ROUNDOFF errors, which I'll ask Phil's advice on, but once they've been cleared, I think it's only unconnected, engracio and Phil with tests below the magic number.

philmoore · 2011-02-10, 04:29

I have started strong probable prime tests, but I realize now that it will take me 5 weeks to finish all 20 tests on my Pentium D. Justin, how on earth did you finish your double-check so fast? I know I am running on old technology, but I did not realize that I was so out-of-date!

I am running a test on pfgw using a SCRIPT file. If anyone wants to volunteer to run some of these tests and speed up the verification, more power to you! The problem is basically to compute base^(2^9092391+20145) mod 2^9092392+40291 and see if the result is equal to 1 or -1 mod 2^9092392+40291. I am running these tests using pfgw and a SCRIPT file. The other tests have been run with all prime bases from 2 to 73, I have queued bases 2, 3, 5, and 7, but if anyone wants to run another base, post here and I can reserve it for you. I will also post my SCRIPT file tomorrow in case you want to use this method, but you may also be able to use pfgw by running an Euler test. I am not sure of what the current pfgw capabilities are.

mdettweiler · 2011-02-10, 05:06

Quote:

Originally Posted by philmoore

I have started strong probable prime tests, but I realize now that it will take me 5 weeks to finish all 20 tests on my Pentium D. Justin, how on earth did you finish your double-check so fast? I know I am running on old technology, but I did not realize that I was so out-of-date!

I am running a test on pfgw using a SCRIPT file. If anyone wants to volunteer to run some of these tests and speed up the verification, more power to you! The problem is basically to compute base^(2^9092393+20145) mod 2^9092394+40291 and see if the result is equal to 1 or -1 mod 2^9092394+40291. I am running these tests using pfgw and a SCRIPT file. The other tests have been run with all prime bases from 2 to 73, I have queued bases 2, 3, 5, and 7, but if anyone wants to run another base, post here and I can reserve it for you. I will also post my SCRIPT file tomorrow in case you want to use this method, but you may also be able to use pfgw by running an Euler test. I am not sure of what the current pfgw capabilities are.

What about just using:

pfgw -tc -q2^9092392+40291

That will perform a combined N-1/N+1 primality test, which of course will not totally succeed since neither N-1 or N+1 can be trivially factored, but the test still produces strong Fermat and Lucas PRP verification.

engracio · 2011-02-10, 05:30

@Jeff I hear you about being lucky.

@enderak and paleseptember my rerun on a different computer for the prime won't be done until Fri morning. Several hours of power outage (only my block) did not help All other wu below the prime should be done by then too.

I am sure as others that the prime will be verified, just when.

Still happy we have found it sooner than later.

enderak · 2011-02-10, 07:16

Phil, my double-check was done on an Intel i7 965 running on all 4 cores at once. If you can give me direction I would be happy to help with the pfgw tests. (Running 64-bit Windows OS)

Should I run it per mdettweiler's suggestion or can you e-mail your script file with directions to use? If the various tests can be split up, I have a few i7's available that could greatly reduce the test time. (Who ever said that patience is a virtue?)

akruppa · 2011-02-10, 09:33

Here's one factor of PRP-1: 2425284208751 (edit: aside from the trivial 2 and 7)

Nothing to write home about but it's a start.

2011-02-10, 00:38	#16
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 17·251 Posts	Congratulations on (probably ) proving the conjecture this project set out to prove! Next step is to wait for incredibly fast computers, or maybe quantum computer factoring for N-1/N+1, or maybe a new primality proving algorithm that makes ECPP look slow, and you can actually prove that these PRPs are all prime and that the conjecture is proven. Well, you can always keep edging up the lower end of proving the PRPs up slowly in the mean time. Last fiddled with by Mini-Geek on 2011-02-10 at 00:53

2011-02-10, 04:29	#18
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 3·373 Posts	I have started strong probable prime tests, but I realize now that it will take me 5 weeks to finish all 20 tests on my Pentium D. Justin, how on earth did you finish your double-check so fast? I know I am running on old technology, but I did not realize that I was so out-of-date! I am running a test on pfgw using a SCRIPT file. If anyone wants to volunteer to run some of these tests and speed up the verification, more power to you! The problem is basically to compute base^(2^9092391+20145) mod 2^9092392+40291 and see if the result is equal to 1 or -1 mod 2^9092392+40291. I am running these tests using pfgw and a SCRIPT file. The other tests have been run with all prime bases from 2 to 73, I have queued bases 2, 3, 5, and 7, but if anyone wants to run another base, post here and I can reserve it for you. I will also post my SCRIPT file tomorrow in case you want to use this method, but you may also be able to use pfgw by running an Euler test. I am not sure of what the current pfgw capabilities are. Last fiddled with by philmoore on 2011-02-10 at 17:37 Reason: corrected the exponents

2011-02-10, 09:33	#22
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Here's one factor of PRP-1: 2425284208751 (edit: aside from the trivial 2 and 7) Nothing to write home about but it's a start. Last fiddled with by akruppa on 2011-02-10 at 09:35

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
probable largest prime.	sudaprime	Miscellaneous Math	11	2018-02-05 08:10
Hi, how can I test my probable prime number?	mohdosa	Information & Answers	22	2014-10-10 11:34
Megadigit probable prime found, our third!	philmoore	Five or Bust - The Dual Sierpinski Problem	25	2009-09-09 06:48
Another record probable prime found!	philmoore	Five or Bust - The Dual Sierpinski Problem	15	2009-02-08 19:43
Record probable prime found!	philmoore	Five or Bust - The Dual Sierpinski Problem	18	2009-01-28 19:47

2011-02-09, 22:57	#15
MooMoo2 Aug 2010 3²×71 Posts	Congrats! Just out of curiosity, will this forum be placed in the "Archived projects" section when all doublechecks are complete?

2011-02-10, 00:55	#17
paleseptember Jun 2008 Wollongong, .au 183₁₀ Posts	Fantastic work! I come back from holidays to find that the project has (almost certainly) been wrapped up! My workunits have finished (no PRPs, no ninja'ing), and have just been emailed off to Phil. I had some ROUNDOFF errors, which I'll ask Phil's advice on, but once they've been cleared, I think it's only unconnected, engracio and Phil with tests below the magic number.

2011-02-10, 05:30	#20
engracio May 2007 11² Posts	@Jeff I hear you about being lucky. @enderak and paleseptember my rerun on a different computer for the prime won't be done until Fri morning. Several hours of power outage (only my block) did not help All other wu below the prime should be done by then too. I am sure as others that the prime will be verified, just when. Still happy we have found it sooner than later.

2011-02-10, 07:16	#21
enderak Feb 2009 3×13 Posts	Phil, my double-check was done on an Intel i7 965 running on all 4 cores at once. If you can give me direction I would be happy to help with the pfgw tests. (Running 64-bit Windows OS) Should I run it per mdettweiler's suggestion or can you e-mail your script file with directions to use? If the various tests can be split up, I have a few i7's available that could greatly reduce the test time. (Who ever said that patience is a virtue?)