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Let $p_n$ be the $n$-th prime number and $Q_a(N)$ be the number of primes of the form $p_n^2+a$ where $1\leq n\leq N$ and $a$ is positive and even. For some $a$ like $26,56$ there seems to no solutions to $p_n^2+a\in\mathbb N$, for some $a$ like $2,8$ there seems to be a unique solution and for s...