## Investigating the primality of numbers of the form 2`n`^{2}-1

### Problem 216

Published on Friday, 7th November 2008, 05:00 pm; Solved by 2759; Difficulty rating: 45%Consider numbers `t`(`n`) of the form `t`(`n`) = 2`n`^{2}-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 ?