Vipul at 01:58, 2 May 2010

2010-05-02T01:58:12Z

← Older revision		Revision as of 01:58, 2 May 2010
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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==

Vipul: Created page with '==Statement== For every natural number $n$ , there exist infinitely many prime numbers $p$ such that the fact about::prime gap between $p$
2010-05-02T01:55:06Z

Created page with '==Statement== For every natural number <math>n</math>, there exist infinitely many prime numbers <math>p</math> such that the fact about::prime gap between <math>p</…'

New page
==Statement==

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>.

==Relation with other facts/conjectures==

===Stronger conjectures===

* [[Weaker than::Hardy-Littlewood conjecture]]

===Weaker facts and conjectures===

* [[Stronger than::Twin primes conjecture]]
* [[Stronger than::Goldston-Pintz-Yildirim theorem on prime gaps conditional to Elliott-Halberstam]]