fond of a factor? Urn yourself to become remains

[ET_]

Originally Posted by axn

Huh? It used to be that, once upon a time, p95 used to go ahead with TF even if a factor was found, just to make sure that no _smaller_ factor was missed. Then, that was removed. You mean to say that this (mis)feature has been reintroduced?!

I'm afraid I followed the wrong chain of answers.
The old behavior was removed.

The actual Prime95 should finish its bit range even if a factor is found.

Luigi

[lorgix]

Which raises my question, again.

Why multiply them?

Isn't that sort of the opposite of what we're trying to do here?

[petrw1]

Originally Posted by alpertron

My computer found the following results:

M120247 has a factor: 3250729890896242123679136285673

Some work effort quantification trivia complements of:
http://mersenne-aries.sili.net/credi...tton=Calculate

Finding the same factor via TF would take over 8.5 quadrillion GhzDays

[cheesehead]

Originally Posted by lorgix

Which raises my question, again.

Why multiply them?

Exactly which ones are you referring to, and which procedure found them? Perhaps there's some mixup.

TF doesn't multiply them. (I've seen TF report two found factors from a single run; it did so on separate "has a factor" lines, not presented as the product of the two.)

P-1, by its nature, may find the product of two smaller factors at the conclusion of its GCD, rather than finding the two separately. Isn't that the method involved in the case you reference?

Isn't that sort of the opposite of what we're trying to do here?

[lorgix]

Originally Posted by cheesehead

Exactly which ones are you referring to, and which procedure found them? Perhaps there's some mixup.

Post #46.

TF doesn't multiply them. (I've seen TF report two found factors from a single run; it did so on separate "has a factor" lines, not presented as the product of the two.)

That's what I'd expect. Hence the question; why multiply?

P-1, by its nature, may find the product of two smaller factors at the conclusion of its GCD, rather than finding the two separately. Isn't that the method involved in the case you reference?

No, as you know by now; he claims it was found by TF. In post #51 I wrote that I thought it would have stopped after finding the smaller one. But that I wouldn't at all be surprised to see that factor found by P-1.

[drh]

This is my largest factor so far-

52526609 has a factor: 156325851414571040867100443817329068296081239222450719

Found by P-1

[lorgix]

That's a composite; p24*p30. Still, nice find!

[Mr. P-1]

Originally Posted by Mini-Geek

These "k=2" you are talking about are really k=1. Factors are of the form 2kp+1. In other words, they're mp+1, with m always even. With these factors, m=2 and k=1, since the factor is equal to 2*p+1.
I'd bet that the factors of the k's break down, on average, like the factors of any natural number of about their size. And that the chance of any given k producing a factor is related to the equation given at http://www.mersenne.org/various/math.php: "(how_far_factored-1) / (exponent times Euler's constant (0.577...))".

That's probably the case for other k. However it is a theorem that if p is a prime congruent to 3 (mod 4) then 2p+1 divides Mp iff 2p+1 is prime. This must affect the statistics.

I'm not aware of any comparable theorem for other k.

[Mr. P-1]

Originally Posted by lorgix

That's a composite; p24*p30. Still, nice find!

Yes. I tend to view composite factors as two factors, rather than as a big factor. Still a P30 is not to be sniffed at

[Mr. P-1]

M39375727 has a factor: 13698938687421045884119517033
M42516611 has a factor: 124316222847533124840651137

The second half of last year was really poor for me. I got no factors at all between 8 August and 26 November. Then three in December, and these two-in-a-row this month.

M39787039 has a factor: 1700513525404800279754718890351

A nice p31 found back in February last year.

[drh]

I also agree that we should view composite factors as two smaller ones. Here is my 2nd largest one, also found by P-1:

M51443083 has a factor: 25320591696138535897675469195834877349466521

I'm also assuming that this is composite since it is so large. I'm still very new at this, and learning. Can you tell me what you are doing, or using to tell if these numbers are composite or not?

Also, maybe I'm getting more than my share, but I've been doing P-1 work for 18 months now, and I've found 24 factors in 331 tests, at about a 7.25% rate.

Thanks,
Doug