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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.

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    See http://mathoverflow.net/questions/74576/infinite-number-of-prime-pairs2012-03-07

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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.

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    We not only "know" that there are infinitely many such primes, we even have a simple formula that tells us, as a function of $x$, approximately how many such primes there are with $p\lt x$. The formula is very close to the actual counts for even the largest values of $x$ for which calculations have been done. For more information, search for Dickson's conjecture.2012-03-06