Factoring/P-1 Benefit question

[JuanTutors]

I was just wondering, is the cost/benefit calculation for how much factoring gets done to a Mersenne number based on the assumption that the number will be LL tested twice, or just once?

[lavalamp]

Twice.

Normally I'd link you to the maths page on mersenne.org now, but looking up, copying and pasting links on a phone takes more than the tenth of a second it would take on a real PC. I'm sure you can find it short order anyway, it's in one of the lower down sidebar sections I believe.

[axn]

Originally Posted by dominicanpapi82

I was just wondering, is the cost/benefit calculation for how much factoring gets done to a Mersenne number based on the assumption that the number will be LL tested twice, or just once?

Twice. Actually, more like 2.032 times (small probability of triple check).

EDIT:- Probably I'm wrong about the 2.032, but I seem to recall such a figure having some significance.

[otutusaus]

This is the formula used (Last Updated: September 1, 2009):

factoring_cost < chance_of_finding_factor * 2 * primality_test_cost

You can find the whole explanation in the following link:
http://www.mersenne.org/various/math.php

[cheesehead]

Originally Posted by dominicanpapi82

I was just wondering, is the cost/benefit calculation for how much factoring gets done to a Mersenne number based on the assumption that the number will be LL tested twice, or just once?

It depends on whether or not there's already been a LL test done. If the factoring is being done preliminarily to a DC, its cost is balanced against just one LL test (plus a fraction for errors).