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We call a prime $p$ "good" if there is $0<k<\log p$ with $2kp+1$ prime. What is the asymptotic density of good primes?

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  • $\begingroup$ What is being chosen randomly here - I guess $p$? How is $p$ chosen randomly? $\endgroup$
    – Will Sawin
    Commented Sep 4, 2021 at 17:16
  • $\begingroup$ I modified my message. Thanks $\endgroup$ Commented Sep 4, 2021 at 17:26
  • $\begingroup$ Call a prime $p$ "good" if there is $k < \log p$ with $2kp+1$ prime. You're asking for the relative asymptotic density of good primes. $\endgroup$ Commented Sep 4, 2021 at 17:51
  • $\begingroup$ It's a better way to ask my question ...Thanks $\endgroup$ Commented Sep 4, 2021 at 18:51
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    $\begingroup$ The density of all primes is zero, so as asked, the question is trivial. I think you are more interested in how many good primes there are up to $x$, asymptotically as $x\to\infty$. $\endgroup$
    – GH from MO
    Commented Sep 4, 2021 at 20:41

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