Szymanski's conjecture

Szymanski's conjecture refers to a problem in the field of number theory, particularly concerning prime numbers. Specifically, it conjectures the existence of infinitely many primes of a certain form related to the sequence of prime numbers. The conjecture states that for any integer \( n \geq 1 \), there are infinitely many primes of the form \( p_k = k^2 + n \) for some positive integer \( k \).