mersenne.ca

[James Heinrich]

Originally Posted by masser

I gotta have more frying pan!

Hmm... that was kinda weird. I think that was more the server's fault than mine.

How's that now?

[masser]

Originally Posted by James Heinrich

Hmm... that was kinda weird. I think that was more the server's fault than mine.

How's that now?

Looks great now. Thanks!

[gLauss]

Originally Posted by James Heinrich

I can easily add in the worktodo lines, but I'm uncertain how to pick appropriate bounds. For those that have been following this more closely please offer guidance. Right now I'm just copying the Pminus1 bounds.

Based on my gutfeeling (which is similiar to George's gutfeeling), you should do the following:

1) If there is already some ECM done, then use a substantially higher bound than the B1 for the current ECM level done. Just use a fixed factor of e.g. 50x which is around 10 digits for ECM.
2) B1 of P+1 should not be as large as the B1 of the P-1 and the P-1 should be run before. I think one half or one third of the P-1 B1 should be used for P+1.
3) If there is no ECM done yet, then choose half or a third of the B1 of the already done P-1.
4) I always let Prime95 choose the B2 bounds (put "0" there).
5) If there has been P+1 work done before (maybe to lower bound), then you should vary the "nth-run" parameter to change the starting value. This increases chances to find factors.


I very much would like if mersenne.ca has a feature like:

• You can choose a single or a small range of exponents.
• Mersenne.ca calculates whatever is best to find a factor and gives it in worktodo.txt format. This can be P-1 work, P+1 or ECM.

Additionally, for the "morefactors.php" file, I would like to be able to change the 1.3x hardcoded value to something much larger. If you increase B1 only in 1.3x steps, then one wastes almost three quarters (1/1.3) of effort on every increase. I usually increase by a factor of 10x (or I don't do that number at all).

[James Heinrich]

Originally Posted by gLauss

Based on my gutfeeling (which is similiar to George's gutfeeling), you should do the following:

This is the kind of bounds-selection logic that should (and presumably, eventually, will) be set by getting assignments from PrimeNet. The kind of values it uses (e.g. "50x current ECM level") are not stored directly in any of my data. Also it's the kind of logic flow that a human can easily make subjective decisions on what bounds make sense and what kind of data is an outlier and should be ignored.

I don't have the expertise at this point to make a tool as you describe to translate an exponent into a most-appropriate worktodo line, sorry.

[gLauss]

Originally Posted by James Heinrich

I don't have the expertise at this point to make a tool as you describe to translate an exponent into a most-appropriate worktodo line, sorry.

Don't worry. I have tried to write a Python script which would consider all the P-1, TF and ECM information available for a given exponent and then decide what is best next, but it is very hard to calculate the odds exactly. I totally understand why you cannot do it, this is just a hobby for all of us.

[James Heinrich]

My very simple P+1 page now shows a list of only factors found by P+1 (if you want the list of all no-factors P+1 efforts see the linked report on mersenne.org), but it does show whether the discovered factor is P+1 smooth or P-1 smooth, data which is not so readily available on mersenne.org
I'm not sure if it's possible for a factor to be both P+1 and P-1 smooth, but if one is found it will highlight that too.
https://www.mersenne.ca/pplus1.php

[nordi]

Originally Posted by James Heinrich

I'm not sure if it's possible for a factor to be both P+1 and P-1 smooth

It is possible. The new factors for M1,924,751 and M92,419 are P+1 smooth and also reasonably P-1 smooth.

[nobreadsticks]

just a small question. what's the difference in "Remaining cofactor is a probable-prime" and "Remaining cofactor is a certified-prime". M78737 shows the former, while M82939 shows the latter, but I don't see what makes the difference.

[LaurV]

Did you try googling "probable prime"?

A probable prime is a number that passes a test which all prime numbers pass, but the number itself can be a prime, a provable composite number, or we may have no freaking idea if it is composite and how to prove it. Or we know how to prove it, but it will take a very long time, and the effort is not worth. The "certified primes" are numbers we know for sure are prime, and we can provide a "certificate" (proof) for the fact they are prime.

[nobreadsticks]

I understand the concept of a probable prime, try not to be condescending to a simple question next time. Was just wondering why the two remaining cofactors that are similar in length differ in whether or not they can be certified primes easily or not

[James Heinrich]

Certification of Probable Primes into actual certainly-primes is (as I understand it) usually done outside the scope of GIMPS and tracked by factordb.com
The Mersenne Number Factored thread usually posts when a new Mersenne number becomes fully factored (with a probable prime) and if/when said PRP is certified really-prime. GP2 has also take charge of maintaining that list on mersenne.ca since he already tracks such things. As right now the cofactor of M82939 is certified-prime, but nobody has uploaded a primality proof for the cofactor of M78737 to factordb.com, hence it remains a "probable" prime.