Purpose of p-1 factoring

[drew]

I don't understand. I thought the purpose of P1 factoring was to weed out exponents with smaller factors, thereby eliminating the need for some lengthy LL tests. If it's already been LL tested, what's the point of P1 factoring?

[dave_0273]

(My appologies for moving your thread. It was just that I would prefer to keep blocks of work from having posts in them that don't specifically relate to that block of work. Please feel free to start new threads though.)

These exponents have only been LL tested once. Before we can verify that an exponent is not prime, we (GIMPS) must have 2 matching residues. This is due to the fact that about 1.6% of all LL tests are bad.

(I think that it is 1.6% of all LL tests, or it could be 1.6% of LL tests with a 00000000 error code)

Therefore, each exponent has to be double checked. We go ahead of the leading edge of double checking doing further factoring on these numbers to see if we can find a factor. If we can, we eliminate the need for the lengthy LL double check. Also, if the original test (or the double check) was wrong, we have also eliminated the need for a triple check.

Also, making a sweeping generalisation here, the majority of computer assigned to doublechecking are older, slower computers. These older computers don't usually have the required RAM to run a p-1 test, so once again it will be skipped (or simply won't run stage 2).

Therefore, we at mersenne-aries try to p-1 all these exponents before they go to primenet for doublechecking. I don't have up to date numbers, but off all the exponents that i have p-1ed, I find a factor about 4.5% of the time. That is ALOT of p90 hours saved.

Ideally, it would have been better if these exponents were p-1ed BEFORE their first LL test, rather than after like we do, but at the end of the day, a factor is a factor.

edit to include some stats

According to James Heinrich's stats site...
I have spent 56.5 p90 hours p-1ing
I have saved 331.8 p90 hours

Therefore, I have saved a net of about 275 p90 hours by p-1ing with mersenne-aries

[drew]

Originally Posted by dave_0273

(My appologies for moving your thread. It was just that I would prefer to keep blocks of work from having posts in them that don't specifically relate to that block of work. Please feel free to start new threads though.)

These exponents have only been LL tested once. Before we can verify that an exponent is not prime, we (GIMPS) must have 2 matching residues. This is due to the fact that about 1.6% of all LL tests are bad.

(I think that it is 1.6% of all LL tests, or it could be 1.6% of LL tests with a 00000000 error code)

Therefore, each exponent has to be double checked. We go ahead of the leading edge of double checking doing further factoring on these numbers to see if we can find a factor. If we can, we eliminate the need for the lengthy LL double check. Also, if the original test (or the double check) was wrong, we have also eliminated the need for a triple check.

Also, making a sweeping generalisation here, the majority of computer assigned to doublechecking are older, slower computers. These older computers don't usually have the required RAM to run a p-1 test, so once again it will be skipped (or simply won't run stage 2).

Therefore, we at mersenne-aries try to p-1 all these exponents before they go to primenet for doublechecking. I don't have up to date numbers, but off all the exponents that i have p-1ed, I find a factor about 4.5% of the time. That is ALOT of p90 hours saved.

Ideally, it would have been better if these exponents were p-1ed BEFORE their first LL test, rather than after like we do, but at the end of the day, a factor is a factor.

edit to include some stats

According to James Heinrich's stats site...
I have spent 56.5 p90 hours p-1ing
I have saved 331.8 p90 hours

Therefore, I have saved a net of about 275 p90 hours by p-1ing with mersenne-aries

Thanks for the thorough answer. It makes sense.