Chen's theorem on Goldbach's conjecture: Difference between revisions
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* [[Weaker than::Cai's theorem on Goldbach's conjecture]]: Every sufficiently large even integer <math>N</math> can be written as the sum of a prime less than or equal to <math>N^{0.95}</math> and a number with at most two prime factors. | * [[Weaker than::Cai's theorem on Goldbach's conjecture]]: Every sufficiently large even integer <math>N</math> can be written as the sum of a prime less than or equal to <math>N^{0.95}</math> and a number with at most two prime factors. | ||
===Other related facts=== | |||
* [[Chen's theorem on prime gaps]]: For every positive even integer <math>h</math>, there exist infinitely many pairs <math>(p,p + h)</math> such that <math>p</math> is a [[prime number]] and <math>p + h</math> is either a prime or a semiprime. | |||
Latest revision as of 02:03, 9 February 2010
Statement
Chen's theorem on Goldbach's conjecture states that every sufficiently large even integer can be expressed either as the sum of two primes, or as the sum of a prime and a semiprime (i.e., a number that is a product of two distinct primes).
Relation with other facts/conjectures
Stronger facts
- Cai's theorem on Goldbach's conjecture: Every sufficiently large even integer can be written as the sum of a prime less than or equal to and a number with at most two prime factors.
- Chen's theorem on prime gaps: For every positive even integer , there exist infinitely many pairs such that is a prime number and is either a prime or a semiprime.
