Let $p$ be a prime. Are there infinitely many prime numbers which are of the form $p$$^2$$+$$4$?


closed as off-topic by Saad, Morgan Rodgers, Namaste, José Carlos Santos, Xander Henderson Jul 15 '18 at 18:34

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    $\begingroup$ Where is your attempt? $\endgroup$ – tien lee Jul 15 '18 at 3:30
  • $\begingroup$ 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. $\endgroup$ – Sambo Jul 15 '18 at 3:33
  • $\begingroup$ I just put that, thank you. $\endgroup$ – Pacifica Jul 15 '18 at 3:48
  • $\begingroup$ $p^2+4 \equiv -1(\mod 6)$ 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 Bakshi Jul 15 '18 at 4:31
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    $\begingroup$ Alright, I deleted it. $\endgroup$ – Pacifica Jul 15 '18 at 5:03

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.

  • $\begingroup$ This is a field which has full of conjectures. $\endgroup$ – Pacifica Jul 15 '18 at 6:59

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