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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