Near-square prime

Definition

A near-square prime of type $n^{2} - k$ for fixed $k$ is a prime that can be written in the form $n^{2} - k$ . Note that we consider near-square primes for $k$ not a perfect square, because if $k$ is a perfect square, then $n^{2} - k$ factorizes algebraically.

According to the Bunyakovsky conjecture, for any fixed $k$ not a perfect square, there should be infinitely many near-square primes of the form $n^{2} - k$ .

Occurrence

Value of

k

Polynomial

n^{2} - k

First few prime values

-1

n^{2} + 1

2, 5, 17, 37, 101, 197, 257, [SHOW MORE]

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