Problem 216

Investigating the primality of numbers of the form 2n2-1

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 ?

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