Henk Stokhorst writes:
M(727) is not prime. VME made the claim that they could compute the
first prime following M(727) in two seconds. Just want to know
someone who can do the same trick and what software it takes.
It took less than 2 seconds to find the next sequential prime :
7060034896770543742372772105511569658378384779628943811708504827156734575902
9962497646848024880749924272446637457099914453082421646959773690663827212173
6526607699022870679030143158018123175881930939339869708632591433883
Well, that's only 156 more than M727, so finding it is easy; the
obvious sieve will do it. Verifying it's at least pseudo-prime took
the mers package's ecmfactor program only 1.27 seconds CPU on my Linux
Pentium 200MHz just now, and proving it prime using Morain's ECPP
program took all of 50.9 seconds.
So, even if they are proving it prime, it's not a big advance.
More to the point, a better test, since they're unwilling to reveal
their method, would be to give them some large, strong pseudo-primes
mixed in with known primes of similar size. Anybody care enough to
produce such a set? The composite factors of prime exponent Mersennes
are all base-2 pseudo-primes, but that's not enough; they should
probably be Cunningham numbers (which are pseudo-prime to all bases
that aren't related to their factors).
The only stronger tests that I can think of are making the program
available via a TCP/IP server of some sort, so people like us can give
it arbitrary numbers to check in real time, and a rigorous proof of
the method, which requires making it public.
Will
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