hey the question is
show that there are infinitely many primes of the form 6k + 5. does the method work for 6k + 1.
my answer so far is
suppose there are finite primes of the form 6k + 5
order them such: p(1) < p(2) <....< p(n)
let R = 6(p(1)p(2)...p(n)) + 5
R can't be prime, if it is R > p(n)
R can't be composite as any division will give a remainder of 5
therefore there are infinitely many primes
i think there's something not quite right with it and i can't use Dirichlet's Theorem
kudos for any help!