I conjecture that there does not exist an arithmetic sequence where every number is prime. Put another way, the set
$$S\_{a,b} = \{a + \delta b \ \vert \delta \in \mathbb{N}\}$$
Where $a, b \in \mathbb{N}$

contains *some* composite number. 

I have no idea how to approach such a question. Googling let me to theorems about densities of primes in arithmetic sequences (Green-Tao and the like), but nothing that answers this elementary question.