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Andrica's conjecture is a conjecture regarding the gaps between prime numbers.
The conjecture states that the inequality
holds for all n {\displaystyle n} , where p n {\displaystyle p_{n}} is the nth prime number. If g n = p n + 1 − p n {\displaystyle g_{n}=p_{n+1}-p_{n}} denotes the nth prime gap, then Andrica's conjecture can also be rewritten as
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