For any positive integer 
, there exists a prime
arithmetic progression of length 
. The proof is an extension of Szemerédi's
theorem.
Green-Tao Theorem
See also
k-Tuple Conjecture, Prime Arithmetic Progression, Prime Number Theorem, Szemerédi's TheoremExplore with Wolfram|Alpha
References
Granville, A. "Prime Number Patterns." Amer. Math. Monthly 115, 279-296, 2008.Green, B. and Tao, T. "The Primes Contain Arbitrarily Long Arithmetic Progressions." 8 Apr 2004. http://arxiv.org/abs/math.NT/0404188.Referenced on Wolfram|Alpha
Green-Tao TheoremCite this as:
Weisstein, Eric W. "Green-Tao Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Green-TaoTheorem.html