Green-Tao Theorem

In 2004 Ben Green and Terence Tao proved that for any positive integer \(k\), there exist arithmetic progressions of primes with \(k\) terms:

Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions, Annales of Mathematics, 167 (2008), pp.481-547, doi: 10.4007%2Fannals.2008.167.481.

Note that the following facts. We find some examples of arithmetic progressions of primes with lengh \(6\) or more by using MATLAB.

Length 6-10 green-tao.xlsx Length 6 gt06.m   gt06.csv Length 7 gt07.m   gt07.csv
Length 8 gt08.m   gt08.csv Length 9 gt09.m   gt09.csv Length 10 gt10.m   gt10.csv
The output of gt10.m on the display