Quote:
Originally Posted by yqiang
Hello,
I apologize if this question is utterly stupid, but I was not able to find a FAQ for this anywhere.
I am confused about the records on http://www.loria.fr/~zimmerma/records/ecmnet.html
For example, it lists a prime factor of (78,129) but it does not give the complete factorization of it. Does this mean that someone just split off that particular factor, while the rest is unknown? How do you determine that the rest is not a product of small primes (trial division up to a limit)?
What are the guidelines for submitting records? For example, I used gmpecm to factor 2^600+1 which yielded a prime factor of 88 digits,
<No, it did not. I am sure ECM found smaller factors. The last cofactor
just happened to be a large prime.>
Obviously the last factor found was found trivially after splitting off all the previous factors.
<Obviously!>
Yi

People run ECM on composite numbers that have already had their small
factors removed. Richard Brent keeps track of factorizations of a^n + 1
and a^n1 for a > 12 on his website. One can find known small factors there.
The factorization of 2^600+1 was first found a LONG time ago.
I suggest that you consult the already published tables before burning
more CPU cycles.