Hint: If k and k+1 are pprime-ish, then so are 4(k)(k+1) and 4k(k+1)+1.
Call an integer pprime-ish if each of its prime factors occurs with power two or higher. Prove by induction that there are infinitely many pairs of consecutive pprime-ish positive integers.
I know how to prove that there are infinitely number primes, but am unsure of how to prove this.