Prime-between-squares conjecture

Statement

This conjecture states that for any natural number $n$, there exists a prime number $p$ such that:

$n^{2}<p<(n+1)^{2}$.

Relation with other facts and conjectures

Stronger conjectures

• Cramér's prime gap conjecture

Weaker conjectures and facts

• Bertrand's postulate
• The generalized Riemann hypothesis implies a gap of $O({\sqrt {n}}(\log n))$.