Re: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne Newsletter, issue #18)

[Daran]

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Sent: Saturday, November 24, 2001 6:49 PM
Subject: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne
Newsletter, issue #18)

 But ones factoring benefit calculation might [should would be in
 line with the popular theme of prescribing what's best for other
 GIMPS participants :)] include not only the time savings of
 eliminating the need for one or two L-L tests, but also the extra
 benefit of finding a specific factor.

I can see no way of objectively quantifying this benefit.

 In the GIMPS Search Status table at www.mersenne.org/status.htm the
 march of progress is from Status Unknown to Composite - One LL to
 Composite - Two LL to ... Composite - Factored.

More desireable - whether or not recorded on that page - would be
Composite - Least (or greatest) factor known.  Most desireable (other than
Prime) would be Composite - Completely factored'.

 This reflects the view (with which I agree) that it is more valuable
 to know a specific factor of a Mnumber than to know that a Mnumber is
 composite but not to know any specific factor of that Mnumber.

 So a Factored status is better for GIMPS than a Two LL status, but
 calculations of factoring benefit that consider only the savings of
 L-L test elimination are neglecting the difference between those two
 statuses.  If one consciously wants to neglect that difference ...
 well, okay ... but I prefer to see that explicitly acknowledged.

It seems to be implicitely acknowledged in the way the trial factoring
depths are determined.  If one places a non-zero value on a known factor,
then the utility of extra factoring work on untested, once tested, and
verified composites would be increased.  It would have to be set very high
indeed to make it worth while returning to verified composite Mersennes.

 Richard Woods

Daran G.


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Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne Newsletter, issue #18)

[ribwoods]

Earlier, Brian Beesley wrote:
 Eh? Doesn't it make more sense to concentrate on factoring
 Mnumbers that haven't yet been L-L tested? That way success in
 finding a factor reduces the number of LL tests, as well as
 (eventually) the number of double checks.

... to which Daran G. recently responded:
 Not necessarily.  The marginal benefit/cost ratio of doing factoring
 work on exponant x awaiting a first time test, is twice what it
 would be if exponant x were awaiting a DC.  This does not mean that
 it is greater that doing factoring work on exponant y which is
 awaiting a DC.

But ones factoring benefit calculation might [should would be in
line with the popular theme of prescribing what's best for other
GIMPS participants :)] include not only the time savings of
eliminating the need for one or two L-L tests, but also the extra
benefit of finding a specific factor.

In the GIMPS Search Status table at www.mersenne.org/status.htm the
march of progress is from Status Unknown to Composite - One LL to
Composite - Two LL to ... Composite - Factored.

This reflects the view (with which I agree) that it is more valuable
to know a specific factor of a Mnumber than to know that a Mnumber is
composite but not to know any specific factor of that Mnumber.

So a Factored status is better for GIMPS than a Two LL status, but
calculations of factoring benefit that consider only the savings of
L-L test elimination are neglecting the difference between those two
statuses.  If one consciously wants to neglect that difference ...
well, okay ... but I prefer to see that explicitly acknowledged.

Richard Woods


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