Andrica's conjecture states that, for the n-th prime number, the inequality
Af(n) = − < 1 for all n > 0.
The largest value found for Af(n) is at n = 4 where we have
Af(4) = − = 0.6708734792908092586... .
The search has gown past n = 26 * 10, so it is highly likely the conjecture is true. However, it has never been proven. Past n = 26 * 10, Af(n) appears to be less than 0.0002.
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