V5 credits for trial-factoring

[Graff]

When credit for trial-factoring is assigned, it seems that LMHers who
continue searching to the upper limit even if factors are found don't
get appropriate CPU credit. As it stands ATM, if you fail to find a
factor in a given range you get far less credit than if you find one
or more factors after searching the entire range.

In the examples below, the exponents were trial-factored from
2^56 to 2^63.

The first example is M83728693 for which no factor was found:

Manual testing 83728693 NF 2008-07-24 17:37 0.0 no factor to 2^63 0.0211

The second example is M83729053 for which one factor was found:

Manual testing 83729053 F 2008-07-24 17:37 0.0 124190339516973313 0.0001

Only 0.0001 C2GD credit (because the factor is 56.785 bits, near the bottom of the
search range) even though the full range was searched.

The third example is M83728691 for which three factors were found:

Manual testing 83728691 F 2008-07-24 17:37 0.0 7095143239736076169 0.0151
Manual testing 83728691 F 2008-07-24 17:37 0.0 6826447540875924881 0.0136
Manual testing 83728691 F 2008-07-24 17:37 0.0 1794036397145430497 0.0020

Here the total credit is 0.0307 C2GD, which is more than 0.0211 but
still doesn't seem right.

Perhaps the proper credit for a trial-factoring that examines the
whole range should be something like:

Credit = Range_Credit * ( 1 + n * Factor_Credit)

where
Range_Credit is the credit for searching the range (in the examples, this would be 0.0211 C2GD)
n is the number of factors found in the range and
Factor_Credit is the bonus for finding factors (it is a number in the range 0 < Factor_Credit <= 1 [I would choose this to be 1/3])

So the three examples would net me 0.0211, 0.0281 and 0.0422 C2GD, for
finding zero, one and three factors.

This would require the manual form scripts to recognize (in some
fashion) when the entire range is being searched. (If using Prime95
and the default "stop processing when a factor is found" option
is in use, the formats would be unchanged.)

So rather than reporting:

UID: GrunwalderGIMP/Alpha, M83743633 has no factor to 2^63

one would report something like:

UID: GrunwalderGIMP/Alpha, M83743633 has no factor from 2^56 to 2^63

when no factors are found and

UID: GrunwalderGIMP/Alpha, M83728691 has a factor: 1794036397145430497 in the range 2^56 to 2^63
UID: GrunwalderGIMP/Alpha, M83728691 has a factor: 6826447540875924881 in the range 2^56 to 2^63
UID: GrunwalderGIMP/Alpha, M83728691 has a factor: 7095143239736076169 in the range 2^56 to 2^63

The logic required by the manual submission forms to interpret these modified formats
is trivial.

Just my 2c.

[Prime95]

Since factoring a Mersenne number to find multiple factors is a non-standard activity, I'm not inclined to devote much effort into making sure it is super-accurately credited.

[crash893]

Oh Snap