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

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 ?

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