The prime numbers contain arithmetic progressions of every finite length. Proved by Ben Green and Terence Tao in 2004 by combining techniques from additive combinatorics and ergodic theory, it resolved a long-standing question about structure hidden within the primes.
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StatementThe prime numbers contain arithmetic progressions of arbitrarily great length: for every natural number k there exist arithmetic progressions of exactly k primes. 1 Classification
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Source Green-Tao Theorem (Wikipedia)
Source Green-Tao Theorem (Wikipedia)
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1. Green-Tao Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence (progression-existence clause)
In number theory, the Green-Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
lead paragraph, first sentence (2004 proof-year clause)
In number theory, the Green-Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
Proved By: Ben Green, Lead
In number theory, the Green-Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
Proved By: Terence Tao, Lead
In number theory, the Green-Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
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