Difference between revisions of "Cramer's conjecture"

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'''Cramér'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]], and specifically with the belief that the number of primes in <math>[n,n+\log n]</math> should resemble a Poisson distribution asymptotically.
 
'''Cramér'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]], and specifically with the belief that the number of primes in <math>[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>[N, N+O(\log^2 N)]</math> for primes, where N is your favourite k-digit number.
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If this conjecture is true, one has an [[An efficient algorithm exists if Cramer's conjecture holds|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.
  
# [[wikipedia:Cramér's_conjecture|Wikipedia entry on Cramér's_conjecture]]
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# [[wikipedia:Cramér's_conjecture|Wikipedia entry on Cramér's conjecture]]

Latest revision as of 18:10, 19 August 2009

Cramér'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, and specifically with the belief that the number of primes in [math][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][N, N+O(\log^2 N)][/math] for primes, where N is your favourite k-digit number.

  1. Wikipedia entry on Cramér's conjecture