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

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

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  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Saad, Morgan Rodgers, Namaste, José Carlos Santos, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.

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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
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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. $\endgroup$ – Pacifica Jul 15 '18 at 6:59

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