Peculiar activity in the 1M range...

[petrw1]

I just noticed that the non-prime exponents between 1,000,000 and 1,005,000 have all been quadruple LL tested recently and many of them have had a couple dozen P-1 tests run with progressively larger B1/B2 combos all by the same user. i.e.

1001911 No factors below 2^61 
 P-1 B1=4200000, B2=4300000 
 Verified LL 373C by "David Slowinski" 
 Verified LL 7EB3104CB7A0373C by "Terry S. Arnold" 
 Verified LL 7EB3104CB7A0373C by "Brian J. Beesley" 
 Verified LL 7EB3104CB7A0373C by "Rob_Dee" on 2009-12-23 
 - snip - 
 History no factor from 2^60 to 2^61 by "Sturle Sunde" on 2009-02-15 
 - snip -
 History B1=1100000, B2=11000000 by "Rob_Dee" on 2009-12-15 
 History B1=1200000, B2=12000000 by "Rob_Dee" on 2009-12-15 
 History B1=1400000, B2=1500000 by "Rob_Dee" on 2009-12-16 
 History B1=1600000, B2=1700000 by "Rob_Dee" on 2009-12-17 
 History B1=1800000, B2=1900000 by "Rob_Dee" on 2009-12-18 
 History B1=2000000, B2=2100000 by "Rob_Dee" on 2009-12-19 
 History B1=2200000, B2=2300000 by "Rob_Dee" on 2009-12-20 
 History B1=2400000, B2=2500000 by "Rob_Dee" on 2009-12-21 
 History B1=2600000, B2=2700000 by "Rob_Dee" on 2009-12-22 
 History B1=2800000, B2=2900000 by "Rob_Dee" on 2009-12-23 
 History 7EB3104CB7A037__ by "Rob_Dee" on 2009-12-23 
 History B1=3000000, B2=3100000 by "Rob_Dee" on 2009-12-24 
 History B1=3200000, B2=3300000 by "Rob_Dee" on 2009-12-25 
 History B1=3400000, B2=3500000 by "Rob_Dee" on 2009-12-26 
 History B1=3600000, B2=3700000 by "Rob_Dee" on 2009-12-27 
 History B1=3800000, B2=3900000 by "Rob_Dee" on 2009-12-28 
 History B1=4000000, B2=4100000 by "Rob_Dee" on 2009-12-29 
 History B1=4200000, B2=4300000 by "Rob_Dee" on 2009-12-30

I certainly am not trying to embarrass Rob or anyone ...

If he is choosing to do these assignments - it's a free country.
If, on the other hand, he doesn't understand the testing process he may not be aware that he is essentially doing a lot of unnecessary work.

[markr]

I wonder how many factors they've found? Unfortunately, although PrimeNet tells us who did the unsuccessful factoring efforts, it does not tell us who was successful and found a factor.

[davieddy]

Love the risquee title of this thread

[WVU Mersenneer]

Originally Posted by petrw1

I just noticed that the non-prime exponents between 1,000,000 and 1,005,000 have all been quadruple LL tested recently and many of them have had a couple dozen P-1 tests run with progressively larger B1/B2 combos all by the same user. i.e.


I certainly am not trying to embarrass Rob or anyone ...

If he is choosing to do these assignments - it's a free country.
If, on the other hand, he doesn't understand the testing process he may not be aware that he is essentially doing a lot of unnecessary work.

I have noticed Rob's extraordinarily-diligent efforts to find a factor for the two exponents which bookend M1e6, M999959 and M1000003, and was wondering if his method of increasing the B1 and B2 of his P-1 attempts by 1e6 every day is a clever and good idea, or if he is doing a lot of unnecessary work.

As I know very little about the math involved in Prime95, and understand even less, it seems to me that P-1 testing is successful very rarely due to the unique properties a factor would have to have in order to be found by it: to have all factors of the factor - 1 be less than B1, or only one between B1 and B2. I don't know what the success rate has been for GIMPS's P-1 efforts finding factors, but I expect it to be less than 5%, and not just because bounds are picked which provide the best time-saving and often result in having probabilities of success of 6% and lower.

I factored the factors of the 116 largest factors reported to PrimeNet in order to see what bounds would have discovered them, only 3 had largest P-1 factor less than 9 digits in size. I do realize, however, that P-1 will find any factor of an exponent as long as the factor's factors meet the P-1 criteria, and smaller factors probably are more-likely to do so. I really did the test I did to see if P-1 was at all a good idea to try to find the large factor waiting to be found for M1061.

Still, it seems to me that using P-1 to find factors for M999959 and M1000003 is a bad idea, but by incrementing the search as he is Rob is at least building a cummulative effort and perhaps making the best of a bad situation.

What say you experts, is Rob onto something or using good cycles in a not-so-good way? While I have your "ears" on P-1, would you rather a P-1 tester use a large B1 and let B2=B1, or should one use the recommended B1 and B2 for an exponent?

Best of luck to Rob!

[MatWur-S530113]

Originally Posted by WVU Mersenneer

I have noticed Rob's extraordinarily-diligent efforts to find a factor for the two exponents which bookend M1e6, M999959 and M1000003, and was wondering if his method of increasing the B1 and B2 of his P-1 attempts by 1e6 every day is a clever and good idea, or if he is doing a lot of unnecessary work.

He did a lot of unnecessary work.
But was it a bad idea? This depends on what he wanted.
To find a factor of the Mersenne-number it was a bad idea.
To get many 'GHz-days' on the P-1 top-producer list it was a 'good' idea. It is possible to copy the save-file of prime95 while doing a stage 2 of a P-1 factoring. After finishing the P-1 and posting the result, you can re-copy the save-file and start a P-1 with larger B1 (but only a little bit larger as before). Now you only need to do a stage 1 from the old B1 up to the new B1 which will save some time. But after finishing the new P-1 you will get the same amount of 'GHz-days' from the server as if you did the new P-1 completely. There were already some discussions in some threads about this problems, and I think in the meantime George Woltman is looking for such 'small expandations' of P-1 and subtracts the 'bad GHz-days'

Originally Posted by WVU Mersenneer

As I know very little about the math involved in Prime95, and understand even less, it seems to me that P-1 testing is successful very rarely due to the unique properties a factor would have to have in order to be found by it: to have all factors of the factor - 1 be less than B1, or only one between B1 and B2. I don't know what the success rate has been for GIMPS's P-1 efforts finding factors, but I expect it to be less than 5%, and not just because bounds are picked which provide the best time-saving and often result in having probabilities of success of 6% and lower.

Because of the known congruence q=1 (mod 2p) of a factor of a Mersenne-number the P-1 method is somehow 'related' to the Mersenne numbers. Let me explain it this way:
A P-1 factoring with B1,B2 'knows' about the congruence
A ECM curve with the same boundaries B1,B2 doesn't 'know' anything about this congruence.
Thus a P-1 with B1,B2 is the fastetst ECM-curve with this boundaries and it is the curve with the highest probability to find a factor. But it is only *one* curve, it is not needed to do a P-1 with nearly the same boundaries on a Mersenne-number (or another number) again. If I want to make a new P-1 on a Mersenne-number I'm choosing at least new B1 >= 4* old B1 (most times B1(new)=10*B1(old)) and B2 as large as possible...

Originally Posted by WVU Mersenneer

I factored the factors of the 116 largest factors reported to PrimeNet in order to see what bounds would have discovered them, only 3 had largest P-1 factor less than 9 digits in size. I do realize, however, that P-1 will find any factor of an exponent as long as the factor's factors meet the P-1 criteria, and smaller factors probably are more-likely to do so. I really did the test I did to see if P-1 was at all a good idea to try to find the large factor waiting to be found for M1061.

This is a result, that P-1 is only one curve of ECM. The largest factors of the Mersenne's are found with SNFS, some with GNFS. The most factors up to 73 digit are found with ECM.

Originally Posted by WVU Mersenneer

Still, it seems to me that using P-1 to find factors for M999959 and M1000003 is a bad idea, but by incrementing the search as he is Rob is at least building a cummulative effort and perhaps making the best of a bad situation.

What say you experts, is Rob onto something or using good cycles in a not-so-good way? While I have your "ears" on P-1, would you rather a P-1 tester use a large B1 and let B2=B1, or should one use the recommended B1 and B2 for an exponent?

Best of luck to Rob!

As long as there is no LLT made on the exponent choose the recommened boundaries. If an exponent is LL-tested (and a proven composite) and you simply want to find factors choose the boundaries as high as possible (but higher as the boundaries of an earlier made P-1) depending on the time you want to spent on the number.

greetings
Matthias

[WVU Mersenneer]

Matthias, I do not know how to adequately thank you for the insight and information you have provided me, both on this thread and my M4219 thread. I am always worried about being skewered by Dr. Silverman as well as the other very knowledgable people on this forum because I don't know enough to even form the most basic questions in most cases, but you come along and offer in depth yet easy to follow explanations and do so with a friendly, helpful, and encouraging manner. Truly, thank you.

I have had a busy morning and my brain is even less able to try to understand what you have said, but I will continue trying and hope I will not lose your patience should I have additional questions.

Thank you again.