15 Jul
2003
15 Jul
'03
7:51 a.m.
On Tuesday, July 15, 2003, at 09:13 AM, Ed Pegg Jr wrote:
Timing[PrimeQ[(32*10^6959 - 23)/99]] {198.245 Second, True}
The above is from a Mathematica run. That's better than a 1.5 year run.
Surely you knew this alread, Ed, but for the record: Mma (and Maple etc) use a probabilistic primality testing algorithm ("Rabin-Miller strong pseudoprime"), which can report that a composite number is prime with (very) small probability. The ECPP method took 1.5 years, but it produced a "primality certificate" whose validity can now be checked easily, so there is now a short, rigorous proof that this particular number is prime. --Michael Kleber kleber@brandeis.edu