Firoozbakht conjecture related: ceiling(prime(n)^(1+1/n)) - prime(n+1).

1, 1, 2, 1, 5, 3, 7, 5, 4, 10, 6, 9, 12, 10, 8, 9, 14, 10, 13, 15, 11, 14, 12, 11, 16, 18, 16, 18, 16, 6, 18, 16, 21, 12, 21, 17, 17, 20, 18, 18, 23, 14, 23, 21, 23, 13, 14, 23, 25, 23, 21, 25, 17, 22, 22, 22, 26, 22, 24, 26, 18, 15, 26, 28, 25, 15, 24, 21, 29

1

The Firoozbakht conjecture states that these numbers are always positive. A quintillion is 10^18.

T. D. Noe, Plot of 5000 terms

T. D. Noe, Table of 5000 terms

Alexei Kourbatov, Verification of the Firoozbakht conjecture for primes up to four quintillion, arVix 1503.01744 (Mar 05 2015)

Wikipedia, Firoozbakht's conjecture

(Mma) Table[Ceiling[Prime[n]^(1 + 1/n)] - Prime[n + 1], {n, 100}]

nonn,nice

T. D. Noe, Mar 07 2015