Contrapositive and Contradiction · Superchallenge problem

Suppose the only primes of the form $4k + 3$ were $3, 7, 11, 19$. Then $N = 4\cdot3\cdot7\cdot11\cdot19 - 1 = 17555$ must have a prime factor of the form $4k + 3$ that is not on the list. What is it?