Problem Statement
Are there arbitrarily long arithmetic progressions of primes?
Categories:
Number Theory Additive Combinatorics Primes Arithmetic Progressions
Progress
The answer is yes, proved by Green and Tao [GrTa08]. The stronger claim that there are arbitrarily long arithmetic progressions of consecutive primes is still open.See also [3] and [141].
This is discussed in problem A5 of Guy's collection [Gu04].
Source: erdosproblems.com/219 | Last verified: January 14, 2026