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Cramér-Granville Conjecture

Defining p_0=2, p_n as the nth odd prime, and the nth prime gap as g_n=p_(n+1)-p_n, then the Cramér-Granville conjecture states that

g_n<M(lnp_n)^2

for some constant M>1.

See also

Honaker's Problem, Prime Gaps

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References

Caldwell, C. K. and Cheng, Y. "Determining Mills' Constant and a Note on Honaker's Problem." J. Integer Sequences 8, Article 05.4.1, 1-9, 2005. http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Caldwell/caldwell78.html.Granville, A. "Harald Cramér and the Distribution of Prime Numbers." Scand. Act. J. 1, 12-28, 1995.

Referenced on Wolfram|Alpha

Cramér-Granville Conjecture

Cite this as:

Weisstein, Eric W. "Cramér-Granville Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cramer-GranvilleConjecture.html

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