On Monday 02 October 2006 07:10, [EMAIL PROTECTED] wrote: > > I meant to say: Large prime numbers like Mersenne ones seem to appear > randomly to us because we cannot use the Eratosthem algorithm here: that > would require so LARGE computers. (I've not done the computation, but my > guess is that a computer smaller than Universe could be enough to find > M45.)
Hmm. Our observed universe contains rather less than 10^100 tachyons & baryons. If we store one bit per *yon then M45 is way, way, way beyond our the capabilities of any computer constructable in the observed universe so far as the sieve method is concerned. However there are other algorithms which are rather more efficient, especially when applied to a quantum computer. A QC with "only" 32,582,657 qubits (plus a small amount of conventional memory) could probably find M45 (and all smaller primes) rather quickly by simply eliminating possible factors. > However, for primes larger than a limit, that's not possible. Yup. The limit is at most 2^(10^100) even for a quantum computer making maximum use of every fundamental particle in the universe. Now that's a very large number (even M45 is tiny in comparison). Yet it's still a long way short of infinity. Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
