On 3 May 00, at 14:46, Harald Tveit Alvestrand wrote:
> by now we should have some statistics - is the distribution
> of factors ("one large" versus "all small" or "several large")
> the same for Mersenne candidates as for "general
> composites", or are Mersennes different?
> This may influence the optimal setting of B1 and B2, as well
> as being an interesting result.
This _is_ an interesting question. However since we are dealing with
numbers (k in 2kp+1) which are "general" rather than "special" my
intuition (always dangerous!) would be that the "general" statistical
theory should be well obeyed.
The tested statistical theories relating to prime numbers seem to be
remarkably accurate e.g. one can predict the approximate number of
prime numbers in an arbitray interval which is fairly small in
comparison with the magnitude of the numbers themselves with very
good results with an absolutely minimal computing effort compared to
that needed to actually identify the primes in the interval.
Regards
Brian Beesley
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