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.
