What is the formula for factoring credits?
 

I just learned how easy it is to calculate LL/DC credits using the status chart :geek:

Now that leaves me curious how factoring credits are calculated. Is it just as easy to determine from a similar chart somewhere? :unsure:

The formula is the following and can be infered from the sources of Prime95.

Factoring Credit : Constant * (2^"HowFarFactored"-2^"HowFarItHadAlreadyBeenFactored")/Exponent

Constant for factoring up to 62 5,00000E-17
Constant for factoring up to 63-64 2,17250E-14
Constant for factoring up to 65 and above 1,63100E-14

So for factoring an exponent N from 62 to 68 bits :

(5 E-17 * (2^64 - 2^62) / N) + (2,1725 E-14 * (2^68-2^64) / N)

Jacob

Thanks.

So as I understand it, if I have a Factoring assignment this computes the credits; however, if I have a LL assignment that first determines the exponent needs to be factored more I assume I will get the Factoring credits for this factoring work and then the LL credits once the LL test is done....correct?

As well, I assume what you are talking about here is P-1 factoring. Are credits also awarded for ECM factoring or is that NOT part of the GIMPS initiative?

[QUOTE=S485122;106209]
So for factoring an exponent N from 62 to 68 bits :

(5 E-17 * (2^64 - 2^62) / N) + (2,1725 E-14 * (2^68-2^64) / N)

Jacob[/QUOTE]

Maybe I misunderstand, but as I read your explanation I think the formula should be:

1.63100E-14 * (2^68 - 2^62) / N

I used the constant 1.631E-14 because I am going up to 68 bits, and I am factoring an exponents already factored up to 62 bits.

This gives me a number that matches the credits I actually received lately.

I did mix up the constants :-(

I meant :

2,1725 E-14 * (2^64 - 2^62) / N + 1.631 E-14 * (2^68-2^64) / N = (300566,636 + 4512995,937) / N = 4813562,574 / N

Your formula gives 4738645,735 / N

The difference between your formula and the one I think is the correct one is less than two percent because the first term about 15 times smaller than the second.

You appear to be correct ... the points I got for the last number I factored matches the points your formula came up with.

HOWEVER ... one thing that strikes me as odd is: Since the formula divides by "N", the BIGGER the exponent(N) the FEWER the points that will be awarded (within specified ranges) ?!?! This seems backwards to me :confused:

This is because the bigger the exponent the fewer the potential factors in each interval (63 bits, 64 bits...) Since the factors are of the form 2*k*exponent+1 the number of k to be tried is proportionnal to 2[sup]n[/sup]/(2*exponent). I say proportionnal because some the k values are eliminated before trying, see the [url=http://mersenne.org/math.htm]The Math[/url] page on the GIMPS site. The trial factoring times indeed decrease when the exponent increases.

[quote=petrw1;106763]HOWEVER ... one thing that strikes me as odd is: Since the formula divides by "N", the BIGGER the exponent(N) the FEWER the points that will be awarded (within specified ranges) ?!?! This seems backwards to me :confused:[/quote]Yes, many (maybe most) people think the same thing when they first contemplate a formula for trial factoring credit.

But, for the reason that Jacob gave, it takes about twice as long to TF exponent 18xxxxxx from 2[sup]64[/sup] to 2[sup]65[/sup] as it does to TF exponent 36xxxxxx from 2[sup]64[/sup] to 2[sup]65[/sup], because the lower exponent has twice as many potential [i]2kp+1[/i] factors in that range as the higher exponent has.

Hmmm.....this might clarify something for me.

About a month ago, just for fun, and after learning about the undocumented feature AdvanceFactor, I thought I would try Advancing M1061 from 60 to about 75 BITS. I naively assumed that if I could factor a 40M exponent from 62 to 68 in a day that I could advance M1061 from 60 to 75 bits in a matter of minutes. Well I started it and when it took a few hours to do 1% of 61 BITS I assumed it must be doing a completely different, very intense method of factoring for it to take that long, so I cancelled it.

Now that I, likewise am 1% wiser of the ways of GIMPS was it only that my M1061 experiment doing the same P-1 factoring but with an exponent with SIGNIFICANTLY more factors to test than a 40M range exponent? ... or is it that AND AdvanceFactor uses different a factoring method?

[quote=petrw1;106849]I thought I would try Advancing M1061 from 60 to about 75 BITS. I naively assumed that if I could factor a 40M exponent from 62 to 68 in a day that I could advance M1061 from 60 to 75 bits in a matter of minutes.[/quote]As you now understand, [I]trial-factoring[/I] over that range would take ... a very ... long ... time. (I'm not sure exactly what AdvancedFactor does.)

[quote]Well I started it and when it took a few hours to do 1% of 61 BITS I assumed it must be doing a completely different, very intense method of factoring for it to take that long, so I cancelled it.[/quote]Trial factoring is as "intense" as it gets -- you're trying every possible factor!! No other method is that exhaustive.

Note that TF also tries many non-possible (composite) factors because that's faster than screening out [I]all[/I] composite candidates. Homework question: Why do I say [U]in this context[/U] that composite [I]2kp+1[/I] candidates are not possible factors?

[quote]was it only that my M1061 experiment doing the same P-1 factoring but with an exponent with SIGNIFICANTLY more factors to test than a 40M range exponent?[/quote]I don't know what method AdvancedFactor actually uses. If it were trial-factoring (not P-1), then the answer would be "Yes, M1061 has about 40,000 times as many potential factors in a given fixed range (such as 2[sup]60[/sup] -> 2[sup]61[/sup]) as M4244xxxx has in that range."

[QUOTE=cheesehead;106865]
Note that TF also tries many non-possible (composite) factors because that's faster than screening out [I]all[/I] composite candidates. Homework question: Why do I say [U]in this context[/U] that composite [I]2kp+1[/I] candidates are not possible factors?
[/QUOTE]

Pardon my ignorance but admittedly my interest in prime numbers far exceeds my mathematical theory prowess regarding prime numbers.

In your context is the "k" composite OR the 2kp+1 composite?

For the latter, all non-prime numbers can be factored into 2 or more prime factors. SO, if we find a composite factor then by definition it can be further factored into primes.

For the former, I'll have to think harder.