Re^4: Rotationally Prime Numbers Revisited


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Re^4: Rotationally Prime Numbers Revisited

by hv (Prior)

on Mar 25, 2005 at 12:54 UTC ( [id://442315]=note: print w/replies, xml )

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in reply to Re^3: Rotationally Prime Numbers Revisited
in thread Rotationally Prime Numbers Revisited

Indeed, I'd argue they're more likely to be primes: numbers of the form M(a, p) = (a^p - 1)/(a - 1) form an extended class of Mersenne numbers, and in particular will not share a factor with any M(a, q), q < p, and draw their factors from the restricted set {p, <2kp + 1>}.

I don't know if there's a way to adapt the Lucas-Lehmer test to check directly for divisors in this extended class.

Hugo

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Re^5: Rotationally Prime Numbers Revisited
by tilly (Archbishop) on Mar 25, 2005 at 19:33 UTC

Let's do some heuristics. the 38'th Mersenne prime is 2**6972593-1. Naively from the Prime Number theorem you'd expect to find an average of 22.12 primes in that sequence to that point. We actually got 38. So we got about 70% more primes than we were expecting to have. The limited results that we have for (10**p-1)/9 suggest a similar advantage.

Which is significant, but not astoundingly different than the naive approximation.

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