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