Shanks' Conjecture

Let $p(g)$ be the first Prime which follows a Prime Gap of $g$ between consecutive Primes. Shanks' conjecture holds that

$$\ln[p(g)]\sim\sqrt{g}.$$

See also Prime Difference Function, Prime Gaps

References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 21, 1994.

Rivera, C. ``Problems & Puzzles (Conjectures): Shanks' Conjecture.'' http://www.sci.net.mx/~crivera/conjectures/conj_009.htm.

Shanks, D. ``On Maximal Gaps Between Successive Primes.'' Math. Comput. 18, 646-651, 1964.