Let $p$ be a prime. Are there infinitely many prime numbers which are of the form $p$$^2$$+$$4$?
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1$\begingroup$ Where is your attempt? $\endgroup$– tien leeCommented Jul 15, 2018 at 3:30
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$\begingroup$ Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem. $\endgroup$– SamboCommented Jul 15, 2018 at 3:33
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$\begingroup$ I just put that, thank you. $\endgroup$– PacificaCommented Jul 15, 2018 at 3:48
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$\begingroup$ $p^2+4 \equiv -1(\mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$. $\endgroup$– Abhishek BakshiCommented Jul 15, 2018 at 4:31
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1$\begingroup$ Alright, I deleted it. $\endgroup$– PacificaCommented Jul 15, 2018 at 5:03
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1 Answer
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The easy answer: We don't know.
Check out: https://oeis.org/A045637.
It looks like this problem is open but an answer would follow from us resolving the Bunyakovsky conjecture. You can read up on that here or on wiki.
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$\begingroup$ This is a field which has full of conjectures. $\endgroup$– PacificaCommented Jul 15, 2018 at 6:59