P-1 factoring Q&A thread

2003-12-16, 18:11

After completing the P-1 test, the program started testing for GCD. I got this result:

Code:

Stage 1 GCD complete. Time: 492.051 sec.
Not enough memory available to run stage 2 now.
Will try again at a later time.
Starting Primality test of M[...]

And then it went ahead and started doing the Lucas-Lehmer testing. I have reserved 32 of 256 MB of memory for Prime95 during the day. How much should I increase it by so I won't see this error again? Also, when will stage 2 of the GCD test commence?

Prime95 · 2003-12-16, 18:26

This is normal and nothing to worry about. Stage 2 will run at night when you have told prime95 it can use more memory. In the meantime, it will start the Lucas-Lehmer test assuming that stage 2 won't find a factor (about a 2% chance).

2003-12-20, 11:29

Do you mean a 98 percent chance?

Prime95 · 2003-12-20, 16:33

Oops. Right, a 98% chance it won't find a factor.

Primeinator · 2005-03-10, 13:42

A couple quick questions. I'm currently testing an exponent that will yield a 10,300,000+ digit prime. It is currently 91.35% done with Stage 1 LL. Since it has not found a factor yet, what are the odds that it is prime? Also, since I don't think I have enough memory to do Stage-2, who will do that and who will get credit-should the number turn out to be prime. (not to be stingy, but I wouldn't mind collecting the $50,000

)
Thanks.

-Kyle

Mystwalker · 2005-03-10, 13:54

When you do a Stage1, you don't do a LL test, but P-1 factoring.
As a result, you can only find factors with this test (and thus prove the number non-prime). A LL test is done after Stage2 of P-1 factoring (which can even done with ~20 MB RAM - with lower bounds and hence less chance of success, though).

Concerning the chances, they are said to be near 1/250,000 - depending on factoring attempts already done for that number. So, every completed LL test gives you $0.20 in average (mean value).

blackguard · 2005-03-10, 13:54

If you go to "Test -> Status" you will get a pop-up window telling you the chances that your exponent will yield a prime.

As for the second question, I don't know who gets assigned those double-checks when a prime is found, but if you find that it is a prime and the double (or triple) check verifies that is the case you should receive the credit. Only if you find erroneously that it is a prime and the double check makes this clear you would lose the credit for the discovery (which is fair enough, anyway). At least that is my understanding. Someone please correct me if that is wrong!

[edited] ooops! Mystwalker just gave you a better answer and beat me by a millisecond or so

[/edited]

Uncwilly · 2005-03-10, 14:15

If you are doing the P-1 factoring, you are not proving the number to be prime, you are rather looking for a factor to disprove its primeness. Because, you can't find a prime with P-1, you don't get credit as having found it, therefore you don't share as a discoverer.
If you are doing the L-L primality checking, you do get credit.

To answer blackguard's question about double checking: To ensure that a newly discovered prime is real, Geogre has some volunteers that have access to non-x86 computers that are fast to do double checking.

Primeinator · 2005-03-10, 21:46

Okay thanks. That answers about half of the question. I know you can go to test and status to find out the chances. My question though is since the program is now nearly 92% done with Stage-1, how much have the odds improved? And another question. For an exponent of this size, what is the ideal memory size needed? Thanks.

Mystwalker · 2005-03-10, 22:56

P-1 factoring and LL testing won't have a result until they have completed (with P-1, some factors can already be found after stage1). Hence, the current status doesn't enhance your chances compared to before the beginning of P-1 factoring. After P-1 factoring (stage1 as well as stage2), the chances increase - but I don't know the exact values. Maybe one or two percent...

Concerning the memory requirements for P-1 factoring, there is a table in the readme file of prime95:

Quote:

Exponent Minimum Reasonable Desirable
-------- ------- ---------- ---------
6000000 12MB 23MB 33MB
10000000 19MB 36MB 53MB
33000000 65MB 125MB 185MB

Plus some more text which I don't want to quote here - it's all in the readme file...

So, contrary to my guess above, 65MB are the minimum for a number of that size.

Uncwilly · 2005-03-10, 23:43

Quote:

Originally Posted by Mystwalker

So, contrary to my guess above, 65MB are the minimum for a number of that size.

AFAIK those numbers are for Stage2.

2003-12-16, 18:11	#1
Unregistered 2×3×7×67 Posts	P-1 factoring Q&A thread After completing the P-1 test, the program started testing for GCD. I got this result: Code: Stage 1 GCD complete. Time: 492.051 sec. Not enough memory available to run stage 2 now. Will try again at a later time. Starting Primality test of M[...] And then it went ahead and started doing the Lucas-Lehmer testing. I have reserved 32 of 256 MB of memory for Prime95 during the day. How much should I increase it by so I won't see this error again? Also, when will stage 2 of the GCD test commence?

2005-03-10, 13:42	#5
Primeinator "Kyle" Feb 2005 Somewhere near M52.. 38C₁₆ Posts	Chances A couple quick questions. I'm currently testing an exponent that will yield a 10,300,000+ digit prime. It is currently 91.35% done with Stage 1 LL. Since it has not found a factor yet, what are the odds that it is prime? Also, since I don't think I have enough memory to do Stage-2, who will do that and who will get credit-should the number turn out to be prime. (not to be stingy, but I wouldn't mind collecting the $50,000 ) Thanks. -Kyle

2005-03-10, 13:54	#7
blackguard Jan 2005 Singapore 13 Posts	If you go to "Test -> Status" you will get a pop-up window telling you the chances that your exponent will yield a prime. As for the second question, I don't know who gets assigned those double-checks when a prime is found, but if you find that it is a prime and the double (or triple) check verifies that is the case you should receive the credit. Only if you find erroneously that it is a prime and the double check makes this clear you would lose the credit for the discovery (which is fair enough, anyway). At least that is my understanding. Someone please correct me if that is wrong! [edited] ooops! Mystwalker just gave you a better answer and beat me by a millisecond or so [/edited] Last fiddled with by blackguard on 2005-03-10 at 13:55

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2003-12-16, 18:26	#2
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 2·3·5²·7² Posts	This is normal and nothing to worry about. Stage 2 will run at night when you have told prime95 it can use more memory. In the meantime, it will start the Lucas-Lehmer test assuming that stage 2 won't find a factor (about a 2% chance).

2003-12-20, 11:29	#3
Unregistered 2²·2,213 Posts	Do you mean a 98 percent chance?

2003-12-20, 16:33	#4
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 7350₁₀ Posts	Oops. Right, a 98% chance it won't find a factor.

2005-03-10, 13:54	#6
Mystwalker Jul 2004 Potsdam, Germany 3×277 Posts	When you do a Stage1, you don't do a LL test, but P-1 factoring. As a result, you can only find factors with this test (and thus prove the number non-prime). A LL test is done after Stage2 of P-1 factoring (which can even done with ~20 MB RAM - with lower bounds and hence less chance of success, though). Concerning the chances, they are said to be near 1/250,000 - depending on factoring attempts already done for that number. So, every completed LL test gives you $0.20 in average (mean value).

2005-03-10, 14:15	#8
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 13×719 Posts	If you are doing the P-1 factoring, you are not proving the number to be prime, you are rather looking for a factor to disprove its primeness. Because, you can't find a prime with P-1, you don't get credit as having found it, therefore you don't share as a discoverer. If you are doing the L-L primality checking, you do get credit. To answer blackguard's question about double checking: To ensure that a newly discovered prime is real, Geogre has some volunteers that have access to non-x86 computers that are fast to do double checking.

2005-03-10, 21:46	#9
Primeinator "Kyle" Feb 2005 Somewhere near M52.. 38C₁₆ Posts	Okay thanks. That answers about half of the question. I know you can go to test and status to find out the chances. My question though is since the program is now nearly 92% done with Stage-1, how much have the odds improved? And another question. For an exponent of this size, what is the ideal memory size needed? Thanks.