--- In

primenumbers@yahoogroups.com, "jbrennen" <jfb@...> wrote:

> is floor(sqrt(18)^n) ever prime? :)

Heuristically, it ought to be prime for some large odd power n.

There is no obvious factor in that case and the integral of

1/(2*n*log(18)) diverges for large n.

Since there is no PRP for n < 10^4, we might need to go up

to something like n = 10^4*18^2 to get a half-way decent

chance of a prime, which would explain the smile sign.

As for the larger question: I have no good idea for a

closed form. Did Mills address the question of the

existence, in principle, of such a number A?

David Broadhurst

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