Fermat number
The prime number theorem implies that a random integer in a suitable interval around "N" is prime with probability 1/ln "N". If one uses the heuristic that a Fermat number is prime with the same probability as a random integer of its size, and that "F"5, ..., "F"32 are composite, then the expected number of Fermat primes beyond "F"4 (or equivalently, beyond "F"32) should be