A Exactly 40% !
This number arises as zeta(4)/zeta(2)2.
For each n=1,2,3,..., the probability that
Can the answer 2/5 be proved by elementary means?
This can be regarded as a form of a question attributed to Wagstaff in problem B48 of R.K.Guy's Unsolved Problems in Number Theory (Springer, 1981): “Wagstaff asked for an elementary proof (e.g., without using properties of the Riemann zeta-function) that [the product ofIs there any value of a xillion for which the probability is actually less than 40%?
(p2+1)/(p2-1)over all primes equals 5/2].”