Bear in mind that you can get (very) lucky with Pollard's Rho. It won't perform comparably for all numbers of the same size.
On 16 March 2015 at 09:15, Hans W Borchers <hwborch...@gmail.com> wrote: > Bill, I think it has become clear what I mean. I agree that is > unreasonable to exactly define up to what limit a general-purpose > scientific software should be able to factorize numbers, for example. But I > feel, Julia should be able to act in about the same range as other > comparable systems, like R or Python. > > With its relatively simple demo version of Pollard's Rho, GMP is capable > of factorizing Fermat's number F6 = 2^(2^7) + 1 = 59649589127497217 * > 5704689200685129054721 within 200 secs (on a slow computer). More > specialized systems like Python/SAGE or PARI/GP do F8 (with 77 digits) in > less than a second (with hand-made C code, I guess). > > I think factorization in the range of 30-50 digits could be possible with > Julia. I will write my own version of Pollard (with Brent's cycle-finding > approach) and see how far I get. If Julia sticks with trial division, fine > with me. Thanks, at the moment I'm not interested in C versions. >
