Near-square prime

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A near-square prime of type  for fixed  is a prime that can be written in the form . Note that we consider near-square primes for  not a perfect square, because if  is a perfect square, then  factorizes algebraically.
According to the Bunyakovsky conjecture, for any fixed  not a perfect square, there should be infinitely many near-square primes of the form .
Value of  Polynomial  First few prime values
-1  2, 5, 17, 37, 101, 197, 257, [SHOW MORE]View list on OEIS