What is the conjectured distributional behavior of semiprimes $pq$ ($p$ and $q$ are primes) having the property $2pq+1$ and $2pq-1$ are primes?
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4$\begingroup$ Clearly one of $p,q$ must be $3$, so this just asks for density of primes such that $6p\pm 1$ are prime. Naive heuristic suggests that up there should be $\asymp\frac{x}{(\log x)^3}$ such primes up to some bound $x$ $\endgroup$– WojowuJan 3, 2023 at 16:37
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