# Near-square prime

From Number

## Definition

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 .

## Occurrence

Value of | Polynomial | First few prime values |
---|---|---|

-1 | 2, 5, 17, 37, 101, 197, 257, [SHOW MORE]View list on OEIS |