2 little questions

[Axel Fox]

Hello,

I just started factoring on the 30M to 31M range, and I have a two little questions about the nofactors.cmp file.

First, I noticed that even if you unpack the entire nofactors.cmp file, there doesn't seem to be ANY number that hasn't been factored until at least 2^57. Did someone actually factor every number to this bound or are the numbers that aren't factored at all yet just not included in the file ?

Second, I also noticed that numbers that have been found composite by a Lucas Lehmer test don't get removed from the nofactors.cmp database. Doesn't this mean that some numbers I am factoring, have already been LL Tested and that there's actually no point in factoring those numbers ?

Greetings,
Axel Fox.

[smh]

Originally Posted by Axel Fox

First, I noticed that even if you unpack the entire nofactors.cmp file, there doesn't seem to be ANY number that hasn't been factored until at least 2^57. Did someone actually factor every number to this bound or are the numbers that aren't factored at all yet just not included in the file ?

All numbers are already factored to at least 2^57 by various people. You can check this page for a visual progress of the last two years.

Originally Posted by Axel Fox

Second, I also noticed that numbers that have been found composite by a Lucas Lehmer test don't get removed from the nofactors.cmp database. Doesn't this mean that some numbers I am factoring, have already been LL Tested and that there's actually no point in factoring those numbers ?

It depends on the range you're testing. But above 30M only a few (except around the 10M digits range) exponents have been tested, and those have probably had substancial more factoring done already.

[Axel Fox]

Ok, thanks for answering my questions. ;)

[cheesehead]

Originally Posted by Axel Fox

First, I noticed that even if you unpack the entire nofactors.cmp file, there doesn't seem to be ANY number that hasn't been factored until at least 2^57. Did someone actually factor every number to this bound

Yes, all Mersenne numbers with exponents below 79300000 have been tested for factors below 2^57. LMHers are close to completing all factoring tests to 2^58, I think.

(A terminology warning for any newbies reading this thread, because I'm in an especially picky mood right now: generally, outside discussions of GIMPS factoring efforts, saying a number is "factored" means a specific factor has been found, not just that the number has been (unsuccessfully) tested in an effort to find a factor. But inside such discussions, it is common to use the verb "factor" to mean "test in an effort to find a factor".)

Second, I also noticed that numbers that have been found composite by a Lucas Lehmer test don't get removed from the nofactors.cmp database.

The nofactors.cmp file includes all Mersenne numbers for which no specific factor has yet been found, regardless of whether any L-L test has been done.

If you want to see which numbers have had at least one L-L test determine that they are composite, look in the hrf3.txt and lucas_v.txt files.

Doesn't this mean that some numbers I am factoring, have already been LL Tested and that there's actually no point in factoring those numbers ?

GIMPS's goal is only to determine whether each Mersenne number is prime or composite. That can be accomplished by either (1) finding a specific factor, or (2) running the L-L test which determines compositeness without finding a specific factor. If that goal is all you're interested in, then factoring is just a way to eliminate the necessity for some L-L tests and there's no point in your searching for a factor after the L-L testing is complete. To avoid such unnecessary factoring (if you're not using the Primenet checkout), use the hrf3.txt and lucas_v.txt files to determine whether a number has been L-Led.

But some people (including me) consider finding a specific factor to be of more value than merely determining compositeness. For those people, it is worthwhile to try finding a factor even after the L-L testing is done.

GIMPS records factoring efforts even after L-Ls are done because erasing those records would be detrimental to that second category of people.