How I could assign a trial factorization Prime95?
 

Hello,

I would like to work on trial factorization of 2^1061-1 to extend it from the current state. So far it has been tried up to factors of 2^62. Could you please help me to assign a job for 2^62-2^63 and so far.

Considering the ECM that has been done on it, TF from 2^62 to 2^63 is (nearly) guaranteed to be absolutely useless. This is the line you would add to worktodo.txt to have Prime95 TF it from 2^62 to 2^63, but it tells you to use ECM instead and doesn't let you do it:[code]Factor=1061,62,63[/code]

[QUOTE=bloodIce;204163]Hello,

I would like to work on trial factorization of 2^1061-1 to extend it from the current state. So far it has been tried up to factors of 2^62. Could you please help me to assign a job for 2^62-2^63 and so far.[/QUOTE]You are extremely unlikely to find any factors by trial division.

This number has had so much ECM work done on it that the chance of it having a factor of under 150 bits is somewhere between nil and negligible. You would be wasting your time and your electricity bill.

If you don't understand that claim, or don't believe it, please Google "elliptic curve method".

However, there are many other computations you could perform with a much, much greater probability of achieving a useful result. Quite a few people here could make suggestions, including myself.

Paul

P.S. Don't be dismayed by some of the reactions your proposal may elicit... Developing a thick skin is part of the entry requirements for playing an active part in on-line discussions.

I agree that there is not much reason to check for lower factors, however if we want to be systematic, we should start from somewhere. The argument to continue what is done to 2^62 is that even a small chance that factor in that range exists, that should be checked and eventually eliminated as possibility. The problem is that the server does not recognize my assignment as Factor=1061,62,63 even not as Factor=1061,81,82. My attitude might be close to absolute stupidity, however why not to check systematically (step by step) for factors up to 250 bits if you wish :smile:. Is there another way to assign what I want (do not bother about my electricity bill, but only about my curiosity)?
@xilman: If you have any idea, where I could use my processors better, please let me know. If something more useful can be done, lets do it then :smile:.

If you absolutely feel that you need to do that, you can do it and turn in the result. Since the server won't assign that (since the CPU is better used by doing ECM), it won't give you an assignment key. There are are ways to do the work. If you poke around the forum you may find them. While you are doing that, maybe you can do some ECM. If a factor is found by ECM, it may lead to the complete factorization. 971 (the last of the small expos without a known factor) has a factor of 174 bits. It is a complete waste of time to try a work your way up to that level.

[QUOTE=bloodIce;204245]
Factor=1061,62,63
Factor=1061,81,82 [/QUOTE]

Besides Electricity, are you aware that according to [url]http://mersenne-aries.sili.net/credit.php[/url] ... which is proven reliable

Factor=1061,62,63 - would take 1 core of a high-end Quad much of a year to complete?
Factor=1061,81,82 - ... in the order of 100 Million years?

[quote=petrw1;204251]Besides Electricity, are you aware that according to [URL]http://mersenne-aries.sili.net/credit.php[/URL] ... which is proven reliable

Factor=1061,62,63 - would take 1 core of a high-end Quad much of a year to complete?
Factor=1061,81,82 - ... in the order of 100 Million years?[/quote]
What the heck? A year to TF an exponent from 62 to 63 bits? (Or is the "slight" decrease in primes to test as exponent increases enough to make it take that long at this extreme low end of things?)

[QUOTE=petrw1;204251]Factor=1061,62,63 - would take 1 core of a high-end Quad much of a year to complete?[/QUOTE]You could instead do 2000 curves at B1=1000000000 B2=5000000000 in less than a GHz year.

I would suggest that you ask some who knows what bounds to run, instead of what you have been doing.
[code]History 3 curves, B1=260000000, B2=26000000000 by "THK" on 2010-01-30
History 3 curves, B1=260000000, B2=26000000000 by "THK" on 2010-01-30
History 3 curves, B1=260000000, B2=26000000000 by "THK" on 2010-01-30
History 3 curves, B1=260000000, B2=26000000000 by "THK" on 2010-01-30
History 100 curves, B1=1000000, B2=100000000 by "ANONYMOUS" on 2010-01-30
History 100 curves, B1=1000000, B2=100000000 by "ANONYMOUS" on 2010-01-30
History 100 curves, B1=1000000, B2=100000000 by "ANONYMOUS" on 2010-01-30
History 100 curves, B1=1000000, B2=100000000 by "ANONYMOUS" on 2010-01-30
History 100 curves, B1=1000000, B2=100000000 by "ANONYMOUS" on 2010-01-30
History 100 curves, B1=1000000, B2=100000000 by "ChuckEtienne" on 2010-01-31
History 2 curves, B1=1000000, B2=100000000 by "BloodIce" on 2010-01-31
History 2 curves, B1=1000000, B2=100000000 by "BloodIce" on 2010-01-31
History 100 curves, B1=1000000, B2=100000000 by "BloodIce" on 2010-01-31
History 10 curves, B1=10000000, B2=1000000000 by "BloodIce" on 2010-01-31
History 10 curves, B1=12000000, B2=1200000000 by "BloodIce" on 2010-01-31
History 100 curves, B1=3000, B2=300000 by "BloodIce" on 2010-01-31
History 500 curves, B1=30000, B2=3000000 by "BloodIce" on 2010-01-31
History 100 curves, B1=30000, B2=30000000 by "BloodIce" on 2010-01-31
History 50 curves, B1=300000, B2=300000000 by "BloodIce" on 2010-01-31
History 100 curves, B1=200000, B2=20000000 by "BloodIce" on 2010-01-31
History 10 curves, B1=1000000, B2=100000000 by "BloodIce" on 2010-01-31
History 400 curves, B1=50000, B2=5000000 by "BloodIce" on 2010-02-01[/code]

[QUOTE=mdettweiler;204252]What the heck?[/QUOTE]

What did you expect?:question:

[quote=axn;204254]What did you expect?:question:[/quote]
I expected something more along the lines of the less than half a GHz-day or so that it would take to do a leading-edge exponent to the same level...according to the calculator it would be ~.4 Ghz-days even for just a 2M exponent.

[QUOTE=mdettweiler;204255]I expected something more along the lines of the less than half a GHz-day or so that it would take to do a leading-edge exponent to the same level...according to the calculator it would be ~.4 Ghz-days even for just a 2M exponent.[/QUOTE]

From "The Math" page: [url]http://www.mersenne.org/various/math.php[/url]
[QUOTE]One very nice property of Mersenne numbers is that any factor q of 2^P-1 must be of the form 2kp+1. Furthermore, q must be 1 or 7 mod 8. [/QUOTE]

As the exponents get bigger there are fewer and fewer possible factors to test in a given bit range; hence less time to complete.

Homework:
a. How many 2kp+1 possibilities are there at 62 bits for p=1061?
b. How many for p=2,000,001?
c. What is the ratio? i.e. How many times more work is involved?

1061 is small number in itself and so 2^1061-1 has the illusion of being small however it is over 300 digits long.