Timeline for Primes in arithmetic progression
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2021 at 8:09 | comment | added | Emmanuel Guillemin | For Sophie Germain primes it matters. My question would be a weak version of the conjecture about the infinity of these numbers. | |
| Sep 5, 2021 at 1:13 | comment | added | Gerry Myerson | I'm not convinced that any purpose is served by insisting that $p$ be prime. One could ask for the density (if it exists) of positive integers $n$ such that the smallest prime $q\equiv1\bmod n$ satisfies $(q-1)/n<2\log n$. Does it really matter whether or not $n$ is prime? | |
| Sep 5, 2021 at 0:32 | comment | added | JoshuaZ | One natural way of understanding this question would be to look at the primes with your property less than or equal to x, divide that by $pi(x)$ and look at that limit. | |
| Sep 4, 2021 at 20:41 | comment | added | GH from MO | 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 $x\to\infty$. | |
| Sep 4, 2021 at 20:39 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Sep 4, 2021 at 20:28 | comment | added | mathworker21 | @EmmanuelGuillemin Do you know what "asymptotic density" and "relative asymptotic density" mean? | |
| Sep 4, 2021 at 19:54 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
MathJax: \log
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| Sep 4, 2021 at 19:54 | comment | added | Emmanuel Guillemin | It's done . Asymptotic density or relative asymptotic density ... any answer is welcome. | |
| Sep 4, 2021 at 19:52 | history | edited | Emmanuel Guillemin | CC BY-SA 4.0 |
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| Sep 4, 2021 at 19:47 | comment | added | Wojowu | We don't need to assume "we know" all primes in that range. You only need to clarify you pick $p$ randomly from that interval. Alternatively, following mathworker's suggestion, ask for the relative asymptotic density. | |
| Sep 4, 2021 at 19:38 | comment | added | Emmanuel Guillemin | We suppose we know all prime numbers between $n$ and $2n$. Thus we have a list of numbers and we take one of them randomly. | |
| Sep 4, 2021 at 19:31 | comment | added | GH from MO | What do you mean by "taking randomly a prime number $p$"? What is the probability that you take $p=101$, for example? | |
| Sep 4, 2021 at 18:51 | comment | added | Emmanuel Guillemin | It's a better way to ask my question ...Thanks | |
| Sep 4, 2021 at 17:51 | comment | added | mathworker21 | 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. | |
| Sep 4, 2021 at 17:26 | comment | added | Emmanuel Guillemin | I modified my message. Thanks | |
| Sep 4, 2021 at 17:25 | history | edited | Emmanuel Guillemin | CC BY-SA 4.0 |
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| Sep 4, 2021 at 17:16 | comment | added | Will Sawin | What is being chosen randomly here - I guess $p$? How is $p$ chosen randomly? | |
| Sep 4, 2021 at 16:56 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Sep 4, 2021 at 15:54 | history | asked | Emmanuel Guillemin | CC BY-SA 4.0 |