# Problem 216: Investigating the primality of numbers of the form 2n2-1

![graphic](img216.gif)

Consider numbers t(n) of the form t(n) = 2n2-1 with n > 1. The first
such numbers are 7, 17, 31, 49, 71, 97, 127 and 161. It turns out that
only 49 = 7\*7 and 161 = 7\*23 are not prime. For n ≤ 10000 there are
2202 numbers t(n) that are prime. How many numbers t(n) are prime for n
≤ 50,000,000 ?