TITLE: Prime of the form $4p+1$
QUESTION [6 upvotes]: I have googled this but found nothing. Do we know if there are infinitely many (or finitely many) primes of the form $4p+1$ where $p$ itself prime?
I proved something only for this case of prime and want to know if it covers only finitely many cases or not (at least I know I didn't prove an empty case :) )
Thank you.

REPLY [2 votes]: We "know" that there are infinitely many primes $p$ such that $4p+1$ is prime, in the sense that we are absolutely certain that it is true. However, no one has been able to prove that it is true.