In $2004$, Green and Tao proved the following amazing result on prime numbers:
for any given $N$, there exists an arithmetic progression of length $N$ consisting of prime numbers only.
Tao won a Fields Medal in 2006.
I am wondering, can we use it in any way to find the maximum length of arithmetic progressions consisting of prime numbers only whose initial term is predefined?
$i.e.$ imagine the initial term of the progression is $5$.
How to find out the maximum length of any arithmetic progression consisting only of prime numbers?