Polignac's conjecture: Difference between revisions
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For every [[natural number]] <math>n</math>, there exist infinitely many [[prime number]]s <math>p</math> such that the [[fact about::prime gap]] between <math>p</math> and the next prime is exactly <math>2n</math>. | For every [[natural number]] <math>n</math>, there exist infinitely many [[prime number]]s <math>p</math> such that the [[fact about::prime gap]] between <math>p</math> and the next prime is exactly <math>2n</math>. | ||
In particular, it asserts that there are infinitely many [[fact about::twin primes]], infinitely many [[fact about::cousin primes]], and infinitely many [[fact about::sexy primes]]. | |||
==Relation with other facts/conjectures== | ==Relation with other facts/conjectures== | ||
Latest revision as of 01:58, 2 May 2010
Statement
For every natural number , there exist infinitely many prime numbers such that the prime gap between and the next prime is exactly .
In particular, it asserts that there are infinitely many twin primes, infinitely many cousin primes, and infinitely many sexy primes.