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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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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?

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

Thanks

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.

Thanks

Given a integer $n$, we assume we know all prime numbers between $n$ and $2n$. If we take randomly a prime number $p$, what is the probability that there exists a number $k$ st $k<\log(p)$ and $2kp+1$ a prime number? Same question for $ k<\log^2(p)$.

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

Thanks