Green, Ben and Tao, Terence, The primes contain arbitrarily long arithmetic progressions. Ann. of Math. (2) (2008), 481-547.

Guy, Richard K., Unsolved problems in number theory. 3rd ed., Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp. Section A5 "Arithmetic progressions of primes", p. 25: "It is conjectured that $n$ can be as large as you like. This would follow if it were possible to improve Szemerédi's theorem (see E10). STOP PRESS (04-04-09): Ben Green & Terence Tao have made just such an improvement, and it seems virtually certain that they have proved that you can indeed have arbitrarily long arithmetic progressions of primes", with the table of known progressions and Pritchard's 22-term progression of 1993. Library home: Guy 2004.