What is Andrica's Conjecture?

 

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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