Strategic Double Clicking

[petrw1]

Originally Posted by GP2

No, the 47626037 is the exponent itself. It's the "p" in 2kp + 1

See the mersenne.ca page, the factor should have been found in stage 1 with B1=144511 or higher. The B2 would only be relevant for stage 2.

Not that I doubt anyone but for fun I ran a test with B1=B2=150000 and found this factor.

I don't suspect the P-1 code/math is extremely complicated (not that I really know)
AND P-1 tests tend to finish in hours/days unlike LL tests that can take weeks/months
SO the odds that a hardware glitch drops a bit and causes such an error should have a much lower error rate than LL.

Is there an easy way of looking to see how many P-1 factors were missed over the years and more importantly were there (m)any in recent years?

[Madpoo]

Originally Posted by petrw1

Not that I doubt anyone but for fun I ran a test with B1=B2=150000 and found this factor.

I don't suspect the P-1 code/math is extremely complicated (not that I really know)
AND P-1 tests tend to finish in hours/days unlike LL tests that can take weeks/months
SO the odds that a hardware glitch drops a bit and causes such an error should have a much lower error rate than LL.

Is there an easy way of looking to see how many P-1 factors were missed over the years and more importantly were there (m)any in recent years?

The problem I've had with doing such an analysis is in figuring out for any given factor, what the minimum B1/B2 are that should have found it. If I knew that (and it would need to be something I could calculate in a SQL query to make things simpler), I could figure out a way to compare that to previous P-1 results that didn't find anything and see if there's a fault.

I plead ignorance when it comes to P-1 since it's just one of those things I never took the time to really study, so if anyone could help with the math part of "for factor X you would need at least B1/B2 of yy/zz" that would be a start. :) Bear in mind that in many cases, P-1 was done with only B1 and no stage 2 was run. That was (and still is?) the bare minimum that needed to be done before it would start the LL testing. So I'd probably also want what the minimum B1 would be to find it in just a stage 1 run.

[LaurV]

Originally Posted by Madpoo

if anyone could help with the math part of "for factor X you would need at least B1/B2 of yy/zz" that would be a start

For factor X you have to factor (X-1)/2p. The largest factor of that is the minimum B2 needed, and the second largest is the minimum B1 needed, in case stage 2 is done, and no BrSu extension is used. When only stage 1 is done, P-1 will find the factor if B1 is the largest factor of the contraption above, or larger.

[kladner]

Originally Posted by LaurV

For factor X you have to factor (X-1)/2p. The largest factor of that is the minimum B2 needed, and the second largest is the minimum B1 needed, in case stage 2 is done, and no BrSu extension is used. When only stage 1 is done, P-1 will find the factor if B1 is the largest factor of the contraption above, or larger.

Wow! Thanks for the concise explanation.

[ATH]

Normally for P-1 it is the smoothness of the factor P minus 1 as the name suggest, but I forgot earlier that GIMPS has a modified version because factors are of the form p=2kq+1, and you only need to look at the smoothness of k=(p-1)/(2*q).

For the factor 537933081092334292774343681 of M47626037:

k=537933081092334292774343680 / 95252074 = 5647468432995320320 = 2^9 * 5 * 17 * 29 * 157 * 167 * 1181 * 144511

So B1>=1181 and B2>=144511 will find the factor, or if no stage2 is done then B1>=144511 is needed to find it.

[petrw1]

Originally Posted by Madpoo

The problem I've had with doing such an analysis is in figuring out for any given factor, what the minimum B1/B2 are that should have found it. If I knew that (and it would need to be something I could calculate in a SQL query to make things simpler), I could figure out a way to compare that to previous P-1 results that didn't find anything and see if there's a fault.

I plead ignorance when it comes to P-1 since it's just one of those things I never took the time to really study, so if anyone could help with the math part of "for factor X you would need at least B1/B2 of yy/zz" that would be a start. :) Bear in mind that in many cases, P-1 was done with only B1 and no stage 2 was run. That was (and still is?) the bare minimum that needed to be done before it would start the LL testing. So I'd probably also want what the minimum B1 would be to find it in just a stage 1 run.

Posts 1703-1705 talk about that...if it makes sense to you

[endless mike]

Originally Posted by GP2

M81857519 and M81857537 should be marked suspect, or whatever the procedure was with those bogus Xolotl results. Shift counts are zero, I wonder what produced those bogus FFFFFFFF800000 residues.

Other results by this user/computer show normal-looking residues (for instance M80331397), but all are unverified.

I just finished double checks on 81857537 and 80331397, and both were mismatched. I’m not saying mine are for sure correct; I’ve had my share of bad results. But it could be an avenue for more checking.

[moebius]

For two of my old LL results a triple-check is needed, after that, I only have results beyond the 80 million range.

44436443

44682527

Thx for the attention

[ATH]

Your results were correct.

[GP2]

Originally Posted by ATH

Your results were correct.

Actually I think his results were incorrect, no?

[moebius]

Originally Posted by GP2

Actually I think his results were incorrect, no?

Yes you are right, and since 2018, I let run only PRP tests on the flaky PC.