Green-Tao theorem: Difference between revisions
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==Relation with other facts/conjectures== | ==Relation with other facts/conjectures== | ||
===Stronger facts=== | ===Stronger facts/conjectures=== | ||
* [[Weaker than::Erdős conjecture on arithmetic progressions]] | * [[Weaker than::Erdős conjecture on arithmetic progressions]] | ||
* [[Weaker than::Tao-Ziegler theorem on primes in polynomial progressions]] | * [[Weaker than::Tao-Ziegler theorem on primes in polynomial progressions]] | ||
* [[Weaker than::Zhou's theorem on arbitrarily large arithmetic progressions of Chen primes]] | * [[Weaker than::Zhou's theorem on arbitrarily large arithmetic progressions of Chen primes]] | ||
Latest revision as of 02:07, 2 May 2010
History
This result is a special case of the Erdős conjecture on arithmetic progressions, which states that any large set contains aribtrarily long arithmetic progression. (It is a special case because the set of primes is large).
Statement
This states that for any positive integer , there exists a prime arithmetic progression of length , i.e., an arithmetic progression of length all of whose members are prime numbers.
