Does Prime95 stop when factor is found?
 

I haven't found the answer yet, so I'm starting a new thread. Yes, I'm obviously new to this.

Does Prime95 discard an exponent and request a new one as soon as a factor is found? These are the ones I'm currently testing: [url]http://www.mersenne.org/assignments/?exp_lo=76007713&exp_hi=76007719[/url]

Thanks.

[QUOTE=jovada;439808]Does Prime95 discard an exponent and request a new one as soon as a factor is found? These are the ones I'm currently testing: [url]http://www.mersenne.org/assignments/?exp_lo=76007713&exp_hi=76007719[/url][/QUOTE]

For those exponents, you are doing Lucas-Lehmer (LL) testing. This is a test that determines with certainty whether or not a Mersenne number is prime, but it does so [I]without[/I] searching for factors. There is a mathematical theory for this, but it is too complicated for most of us to understand. The LL test has to run until 100% complete, and then it gives a definite answer.

There are some other tests that can find some factors: trial factoring and P−1 testing, and for smaller exponents also ECM testing. However, for any exponents available for LL testing through the website, those other tests were already run for a certain period of time and did not find any factors, so now LL testing is being done.

Just to expand/clarify the answer that GP2 gave:

The LL test needs to process as many cycles as the size of the exponent (+-1, I forget). Then it produces either a result of all zeros, which means the number is prime, or not zero, which it means it is not prime. For your exponent [B]all[/B] ~76,000,000 iterations must be done to get the result. There is no indication prior to the last step that could give a practical hint.


If one is using Prime95 to do Trial Factoring (this currently checks for factors that are roughly 1/1,000,000th the size of the full decimal form of the number), yes, it will stop when it finds a factor.
Here is an example of a number that had a factor found: [url]http://www.mersenne.ca/exponent/79377841[/url]
It is 23,895,112 decimal digits long. The factor has only 23 digits.

It would be nice if Prime95 stopped if the server knows there's a factor for the exponent.

[QUOTE=Mark Rose;439845]It would be nice if Prime95 stopped if the server knows there's a factor for the exponent.[/QUOTE]

Finding a factor while being LL'ed shouldn't happen though, exponents passed out for LL should already be TF'ed high enough.

[QUOTE=Gordon;439874]Finding a factor while being LL'ed shouldn't happen though, exponents passed out for LL should already be TF'ed high enough.[/QUOTE]

It happened a few times in the final days before the 36M double-check milestone:

[URL="http://www.mersenne.org/report_exponent/?exp_lo=35999687&full=1"]35999687[/URL]
[URL="http://www.mersenne.org/report_exponent/?exp_lo=35872469&full=1"]35872469[/URL]

Some other cases in the 36M range:

[URL="http://www.mersenne.org/report_exponent/?exp_lo=36434863&full=1"]36434863[/URL]
[URL="http://www.mersenne.org/report_exponent/?exp_lo=36494747&full=1"]36494747[/URL]
[URL="http://www.mersenne.org/report_exponent/?exp_lo=37061471&full=1"]37061471[/URL]

In three of the above cases, the LL test ran to completion. In the case of 36434863 and 37061471, the LL test shows expiry on the same day the factor was found.

I think there was a thread somewhere where someone complained that they couldn't get Category 0 exponents anymore because an exponent of theirs got expired when someone else found a factor partway through their LL test, and that meant they no longer met the assignment rules criteria.

[QUOTE=Uncwilly;439843]The LL test needs to process as many cycles as the size of the exponent (+-1, I forget).[/QUOTE]IIRC exponent - 2. M3 needs only one iteration: 4[sup]2[/sup]-2 mod 2[sup]3[/sup]-1 ≡ 0

[QUOTE=GP2;439882]It happened a few times in the final days before the 36M double-check milestone:

[URL="http://www.mersenne.org/report_exponent/?exp_lo=35999687&full=1"]35999687[/URL]
[URL="http://www.mersenne.org/report_exponent/?exp_lo=35872469&full=1"]35872469[/URL]

Some other cases in the 36M range:

[URL="http://www.mersenne.org/report_exponent/?exp_lo=36434863&full=1"]36434863[/URL]
[URL="http://www.mersenne.org/report_exponent/?exp_lo=36494747&full=1"]36494747[/URL]
[URL="http://www.mersenne.org/report_exponent/?exp_lo=37061471&full=1"]37061471[/URL]

In three of the above cases, the LL test ran to completion. In the case of 36434863 and 37061471, the LL test shows expiry on the same day the factor was found.

I think there was a thread somewhere where someone complained that they couldn't get Category 0 exponents anymore because an exponent of theirs got expired when someone else found a factor partway through their LL test, and that meant they no longer met the assignment rules criteria.[/QUOTE]

They are DC's not LL's...

[QUOTE=Gordon;439884]They are DC's not LL's...[/QUOTE]

There might still be a few "lone wolves" hunting factors "extrajudicially" (read: not properly pre-reserved from Primenet) below 100M, but I would be surprised.

There is little point; all needed TF'ing below 71M has already been done, and all below 79M will be done shortly.

[QUOTE=chalsall;439886]There might still be a few "lone wolves" hunting factors "extrajudicially" (read: not properly pre-reserved from Primenet) below 100M, but I would be surprised.

There is little point; all needed TF'ing below 71M has already been done, and all below 79M will be done shortly.[/QUOTE]

I do know when I was double checking TF work from some proven bad machines that I did kill one or two active LL and DC assignments.

I do agree it's unusual though.

[QUOTE=retina;439883]IIRC exponent - 2. M3 needs only one iteration: 4[sup]2[/sup]-2 mod 2[sup]3[/sup]-1 ≡ 0[/QUOTE]

depends on what you call an iteration s0=4;s1=4^2-2 =14 gives two if you count the first one if not.