Journal article

### The primes contain arbitrarily long arithmetic progressions

Abstract:

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemeredi's theorem, which asserts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemeredi's theorem that any subset of a sufficiently pseudorandom set of positive relative density contains progr...

### Authors

Publication date:
2004-04-08
URN:
uuid:992b0869-cbb0-4f1a-8b86-272142e10359
Source identifiers:
398487
Local pid:
pubs:398487
Keywords: