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Infinite or Finite number of primes $p$ such that $p$ has a form:

$p + 1 = \left( {\frac{{k - 1}}{2}} \right)\left( {\frac{{k + 1}}{6}} \right)$ where $k=5 \text{ } (mod \text{ }6)$ ?.

Remark that since $k=5 \text{ }(\text{ }mod\text{ } 6)$, ${\frac{{k - 1}}{2}}, {\frac{{k + 1}}{6}} \in {\rm N}$.

I think that the question is very hard. If anyone gets any ideas, I appreciate it. Thank you!

Nguyen Dang Son
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1 Answers1

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Setting $k=6n-1$, this is equivalent to asking if the polynomial $3n^2-n-1$ takes infinitely many prime values. This is an open problem, a special case of Schinzel's Hypothesis H.

Greg Martin
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