Andrica's conjecture

Andrica's conjecture (named after Dorin Andrica) is a conjecture regarding the gaps between prime numbers.

The conjecture states that the inequality

holds for all ${\displaystyle n}$, where ${\displaystyle p_{n}}$ is the nth prime number. If ${\displaystyle g_{n}=p_{n+1}-p_{n}}$ denotes the nth prime gap, then Andrica's conjecture can also be rewritten as

Imran Ghory has used data on the largest prime gaps to confirm the conjecture for ${\displaystyle n}$ up to 1.3002 × 10¹⁶. Using a table of maximal gaps and the above gap inequality, the confirmation value can be extended exhaustively to 4 × 10¹⁸.

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