Maybe a dumb question but why has trial factoring not been taken further on this number (and other similar numbers)? I get the whole point of that after hitting a certain point you get diminishing returns on CPU time compared to other uses, but I would have thought that someone might use some time on it. Wouldn't be averse to using a core to take some of the lower unfactored numbers further through TF myself, if I can work out the editing of worktodo

ECM has been done to 55-60 digit level on this number, which correspond to trialfactoring to 182-199 bit level.

Anyway this is already being sieved for NFS factoring.

[QUOTE=jonthomson;262929]Wouldn't be averse to using a core to take some of the lower unfactored numbers further through TF myself, if I can work out the editing of worktodo[/QUOTE]There is some work being done on lower numbers. ECM will have the best chance per GHz/day of finding a factor (on those that remain unfactored). TF'ing these numbers with a CPU does not make any sense at the moment.

[QUOTE=Uncwilly;262949]There is some work being done on lower numbers. ECM will have the best chance per GHz/day of finding a factor (on those that remain unfactored). TF'ing these numbers with a CPU does not make any sense at the moment.[/QUOTE]

"best chance" here is not correct.

After Bruce's work and EPFL's latest pass, the chances of finding a factor
from 2^n-1 for n < 1200 is [i]miniscule[/i]. For most of these numbers, ECM
does [b]not[/b] have the "best chance" per GHz/day. Instead, with high
probability, NFS will succeed with less work. And it is guaranteed.

If NFS@Home were to attempt a larger number than M1061, some additional
ECM work might be done on that number as a pre-screen. Otherwise,
further ECM work on these numbers does not have a lot of value.

[QUOTE=R.D. Silverman;262950]"best chance" here is not correct.

After Bruce's work and EPFL's latest pass, the chances of finding a factor
from 2^n-1 for n < 1200 is [i]miniscule[/i]. For most of these numbers, ECM
does [b]not[/b] have the "best chance" per GHz/day. Instead, with high
probability, NFS will succeed with less work. And it is guaranteed.

If NFS@Home were to attempt a larger number than M1061, some additional
ECM work might be done on that number as a pre-screen. Otherwise,
further ECM work on these numbers does not have a lot of value.[/QUOTE]
I was referring to the larger class of numbers, like up to 100,000.

[QUOTE=Uncwilly;262953]I was referring to the larger class of numbers, like up to 100,000.[/QUOTE]

But the original post said:

"Maybe a dumb question but why has trial factoring not been taken further on this number (and other similar numbers)? I get the whole point of that after hitting a certain point you get diminishing returns on CPU time compared to other uses, but I would have thought that someone might use some time on it. Wouldn't be averse to using a core to take some of the lower unfactored numbers"

'This number' is M1061. The reference to 'other similar numbers' and 'lower unfactored numbers' seems to preclude the large exponents you refer to.

'Trial factoring' on any 2^n-1, for n up to at least 2000 is pointless.
Too much ECM and P-1 has been done.

[QUOTE=R.D. Silverman;262955]'Trial factoring' on any 2^n-1, for n up to at least 2000 is pointless.
Too much ECM and P-1 has been done.[/QUOTE]So you agree with my statement: "TF'ing these numbers with a CPU does not make any sense at the moment."

The class that you refer to "up to at least 2000", contains exactly 4 exponents, all of which have had ECM up to B1=260,000,000 (at least 112,000 curves and a factor size of 60 digits). Thus PrimeNet is not handing out new ECM assignments for them.

Since [FONT="Fixedsys"]jonthomson[/FONT] is a newbie to the forum and referring to using 'a core' and the 'worktodo', I figured that he is running Prime95.
Therefore, I was steering him to work that Prime95 can handle. NFS is not such a work type. "[B]ECM on small Mersenne numbers[/B]" is such a work type. Numbers below 10,000,000 are available for this work type and some of those below 6,000,000 are so assigned.

The work type I mentioned is available and easy to use and does not require messing with worktodo files. It is a fire and forget.

[QUOTE=Uncwilly;262973]So you agree with my statement: "TF'ing these numbers with a CPU does not make any sense at the moment."

The class that you refer to "up to at least 2000", contains exactly 4 exponents,
[/QUOTE]

Unfactored 2^n-1 for n < 2000 has only 4 exponents??

Clearly you count differently from the way everyone else does.

[QUOTE=R.D. Silverman;262980]Unfactored 2^n-1 for n < 2000 has only 4 exponents??

Clearly you count differently from the way everyone else does.[/QUOTE]No, he uses "unfactored" in a different way from you. "Unfactored" has as one of its meanings "without any known prime factors". Another meaning is "without being completely factored into primes".

Paul

[QUOTE=xilman;262981]No, he uses "unfactored" in a different way from you. "Unfactored" has as one of its meanings "without any known prime factors". Another meaning is "without being completely factored into primes".[/QUOTE]Correct. And that is a common usage by the crowd that is using Prime95 to work on Mersennes. The latter usage would normally be referred to as "not fully factored". (Not in the number theory and academic world, but out in most of this forum.)

[QUOTE=xilman;262981]No, he uses "unfactored" in a different way from you. "Unfactored" has as one of its meanings "without any known prime factors". Another meaning is "without being completely factored into primes".

Paul[/QUOTE]

The purpose of trial factoring for GIMPS is to eliminate candidates for
LL testing that can be disposed of more quickly by finding a small prime
factor.

The factor itself is irrelevant because it is highly improbable that
the cofactor is prime. Having an objective of finding just one small factor
of a number that is too large to be fully factored is a pointless
waste of time if the objective is JUST that small factor.