confused about scores

[AlanSimpson]

ok, it's not all about scores, but I am definitely confused about this.

Can anyone explain why the following are scored as they are?

The following are from the "Largest factors" section of http://www.aooq73.dsl.pipex.com/ui/2171.htm (with a few columns removed)

p k n Score Factor found Score could be
385.476T 22699 15242518 3.855 Sun 10-Oct-2004 279872.582
385.450T 33661 1145592 948.482 Sun 10-Oct-2004
385.435T 55459 15558826 3.854 Sun 10-Oct-2004 291578.373

Why does the middle one have a much larger score than the other 2. In fact, all the other 26 largest factors have a score that looks like p/100T. Why?

What is the "Score could be" for?

What is the "Factors next to enter (main) 'active window' (@n=7309623)" section on that page for?

I can see that it only contains factors for n>=7309623.

Similarly, the "Factors next to enter (double check) 'active window' (@n=1225808)" section?

thanks,

Alan

[Mystwalker]

Scoring is explained here:
http://www.aooq73.dsl.pipex.com/

The middle test is in the DC active window, thus it will soon save us a DC test.
The other tests are way in front of us, just scoring p/100T, as you've noticed. The "Score could be" column tells you how much points you will get once the active window has increased so much that it now includes the resp. test.
There are as well some tests between DC active window and main active window. Scoring outside the active window is the same, whereas scoring once the DC active window reaches them is only 60% of what one would get for the main active window, as one PRP test has already been done.

The "Factors next to enter ..." tables show which tests soon fall into the active windows, thus the score will increase somewhat, as that is the time the found factors indeed save us a test (or even 2, as it's the case with the main window).

Example:
Take the first line of "Factors next to enter (main) 'active window' (@n=7309623)":

 385.055T  22699   7736230      3.851  Sun 10-Oct-2004  72016.460

Once the upper bound of the main active window reaches n=7736230 (which will take approx. 55 days with current PRP production), the factor's test is in the main active window (which means that soon, it really will save a test) and the score will be changed to 72016.460

The main reason for this scoring schema are the factorers, as they output less factors per time, but factors that almost definitely (see below) saves a test in a few days, whereas factors found with sieving could be worthless for years (n=19M won't be reached soon). If a prime for that k is found in the meantime, the factor is completely worthless. The chance that this happens to 'P-1 factored' factors is very low.

Hope this is understandable...

[Nuri]

Just a little more help.

The logic behind the scoring system is:

- Factors are useful if they save us PRP time.
The more they save, the more points they get.
If they do not save much PRP time, they get lower points.

- Factor densities decrease as sieve depth (p) increases. Thus, there is an adjustment w.r.t. p to enable relatively equal scoring per sieving time.

- Also, P-1 should be encouraged as well. The scoring system tries to take care of that too.


Please also see Placebo shifting effect thread for the discussion on how it was first created.