Cramér Conjecture


The Cramér conjecture is the unproven conjecture that

 lim sup_(n->infty)(p_(n+1)-p_n)/((lnp_n)^2)=1,

where p_n is the nth prime.

See also

Andrica's Conjecture, Brocard's Conjecture, Prime Difference Function

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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: Conjecture 007.-The Cramer's Conjecture."

Referenced on Wolfram|Alpha

Cramér Conjecture

Cite this as:

Weisstein, Eric W. "Cramér Conjecture." From MathWorld--A Wolfram Web Resource.

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