Cramér Conjecture

An unproven Conjecture that

$$\overline{\lim_{n\to\infty}} \,{p_{n+1}-p_n\over(\ln p_n)^2} =1,$$

where $p_n$ is the $n$th Prime.

References

Cramér, H. ``On the Order of Magnitude of the Difference Between Consecutive Prime Numbers.'' Acta Arith. 2, 23-46, 1936.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 7, 1994.

Riesel, H. ``The Cramér Conjecture.'' Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 79-82, 1994.

Rivera, C. ``Problems & Puzzles (Conjectures): The Cramer's Conjecture.'' http://www.sci.net.mx/~crivera/conjectures/conj_007.htm.