Abstract
We discuss the number in the title, especially whether the
minimum period of the Bell numbers modulo p can be a proper
divisor of N_p = (p^p-1)/(p-1). The investigation leads to
interesting new theorems about possible prime factors of N_p.
For example, we show that if p -s odd and q = 4m^2p+1 is prime
and m is a positive integer, then q divides p^{m^2p} - 1.
Then we explain how this fact influences the probability that
q divides N_p
