Peculiar activity in the 1M range...
 

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.

[CODE]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 [/CODE]

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 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.

Love the risquee title of this thread:smile:

[QUOTE=petrw1;200348]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.[/QUOTE]
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!

[QUOTE=WVU Mersenneer;246324]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.[/QUOTE]
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':tu:

[QUOTE=WVU Mersenneer;246324]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. [/QUOTE]
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...

[QUOTE=WVU Mersenneer;246324]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.[/QUOTE]
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.

[QUOTE=WVU Mersenneer;246324]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![/QUOTE]
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

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.