Dear Simon,
I have base about 1 MB prime factors which occured in many
factorizations x^n-1 , Lucas, Fibonacci etc. I don't adding any
successive primes only primes which occured in siome factorizations (my
base also contained Cunningham base and 100 others)
Algorhithm of probe factorziation is very simply. Take successive
primes from base smaller as factorized number and by GCD method checked
that this prime divisor occured in factorized number. GCD algorhitm is
very quick that scan whole baseneed few seconds but finding big factors
even with NFS method (not implemented in SAGE yet) need lot of time.
That is worth lost 5 second on the start and lot of very big numbers can
be factorized completely on this method during 5 seconds only.
Best wishes
Artur
W dniu 2011-11-27 22:33, Simon King pisze:
Hi Artur,
On 27 Nov., 22:08, Artur<[email protected]> wrote:
John,
Many Thanks for support! Now I have all information which I need on the
start.
Good! I think tab completion and the possibility to see documentation
and even the source code of the stuff is a big plus.
About Integer factorizations Will be worthy to implemented to SAGE probe
factorization with prime base to safe computer time.
At least according to the benchmarks at http://sagemath.org/tour-benchmarks.html
(factorization of 2^512-1), Sage is not bad at factoring integers. So,
I guess using the existing implementation of factorization algorithms
is a good starting point. Of course, if you observe that in some
applications factorization is too slow and you know how to improve it,
then you are welcome to demonstrate how.
Cheers,
Simon
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