Cramer's conjecture: Difference between revisions
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New page: Cramer's conjecture asserts that the largest gap between adjacent primes of size N should be <math>O(\log^2 N)</math>. This is compatible with Cramer's random model for the primes, an... |
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If this conjecture is true, one has an easy positive answer to the [[finding primes]] project in the strongest form; one simply searches an interval of the form <math>[N, N+O(\log^2 N)]</math> for primes, where N is your favourite k-digit number. | If this conjecture is true, one has an easy positive answer to the [[finding primes]] project in the strongest form; one simply searches an interval of the form <math>[N, N+O(\log^2 N)]</math> for primes, where N is your favourite k-digit number. | ||
# [http://en.wikipedia.org/wiki/Cram%C3%A9r%27s_conjecture Wikipedia entry on Cramer's conjecture] | |||
Revision as of 09:45, 8 August 2009
Cramer's conjecture asserts that the largest gap between adjacent primes of size N should be [math]\displaystyle{ O(\log^2 N) }[/math]. This is compatible with Cramer's random model for the primes, and specifically with the belief that the number of primes in [math]\displaystyle{ [n,n+\log n] }[/math] should resemble a Poisson distribution asymptotically.
If this conjecture is true, one has an easy positive answer to the finding primes project in the strongest form; one simply searches an interval of the form [math]\displaystyle{ [N, N+O(\log^2 N)] }[/math] for primes, where N is your favourite k-digit number.
