User blog comment:WaxPlanck/Forum:WaxPlanck Prime Numbers/@comment-32783837-20180128024747/@comment-1605058-20180128135859

This is the case for almost all sequences of prime numbers of a specific form (the arithmetic progressions being an exception). Heuristically, for the exponent up to n, we expect approximately log n primes of the form 3k-2, but there is very little progress towards showing that there even are infinitely many such primes.