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

In reply to Re^4: Rotationally Prime Numbers Revisited by hv
in thread Rotationally Prime Numbers Revisited by Limbic~Region

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