Application of the Green-Tao theorem

I am currently trying to find some good exercises in analytic number theory, suitable for undergraduates.

I have mentioned the Green-Tao theorem for arithmetic progressions of primes but I am struggling to find any interesting applications/problems.

Does anyone know of any?

Exercise/Question: Is the Green-Tao theorem also true for composite numbers, i.e., are there arithmetic progressions $an+b$ with $gcd(a,b)=1$ of arbitrarily large length consisting only of composite numbers ? For example, the progression $7n+1$ gives three composite numbers $8,15,22$ for $n=1,2,3$.
Hint: A solution can be found at MSE, question $p=164513$ prime.