> 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).
Do you mean Carmichael numbers ? Carmichael numbers are though not
strong pseudo - primes, since they might fail the strong psp test
already for the first base (the test was designed on this purpose).
Richard Pinch at Cambridge used to be a master of combining strong
psp's - but I think he left Cambridge ...
>
> 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.
>
I bet the last is highly sufficient ....
Sincerely
Preda
> Will
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