--- In

primenumbers@yahoogroups.com,

Sebastian Martin Ruiz <s_m_ruiz@...> wrote:

> 32(n!)**8+1 is composite for all n positive integer ??

On the contrary, the PNT makes it probable (but not yet provable)

that there is an *infinite* number of primes of this form.

The probability that (2*(n!))^8+1 is prime

is (heuristically) asymptotic to exp(Euler)/(8*n).

[If I got the constant wrong, Chris will correct me.]

The integral of 1/n diverges.

Moral: just because you didn't find a small one,

doesn't mean there isn't an infinity of larger ones.

David