Timeline for Are there infinitely many karmic numbers, i.e numbers whose primality radii equal one or a prime power?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2019 at 22:36 | comment | added | Sylvain JULIEN | Let us continue this discussion in chat. | |
| Nov 25, 2019 at 22:34 | comment | added | Wojowu | I don't see how Dirichlet's theorem guarantees this, nor how this is relevant for the problem at hand. | |
| Nov 25, 2019 at 22:33 | comment | added | Sylvain JULIEN | The $n$ from your previous comment, i.e the infinitely many ones that have long arithmetic progressions in their primality radii. | |
| Nov 25, 2019 at 22:22 | comment | added | Wojowu | Which $n$? And how does this follow from Dirichlet's theorem? Didn't we assume $n$ is divisible by $6$? | |
| Nov 25, 2019 at 22:21 | comment | added | Sylvain JULIEN | Doesn't it follow from Dirichlet's theorem that those $n$ are equally distributed among the residual classes modulo $6$ which are not equal to the classes of $1$ or $5$? | |
| Nov 25, 2019 at 22:14 | comment | added | Wojowu | Indeed, Green-Tao implies that infinitely many $n$ will have long arithmetic progressions in their primality radii. But those $n$ will be sporadic, and most likely won't cover all (sufficiently large) multiples of $6$. So you can't deduce from this the claim that large multiples of $6$ won't be sporadic. | |
| Nov 25, 2019 at 22:11 | comment | added | Sylvain JULIEN | $n$ being a karmic number, it implies the number of primality radii of $n$ with $\omega(n)\leq 1$ is the total number of primality radii of $n$ which is an $o(\pi(n))$. But doesn't Green-Tao's theorem imply that the length of some arithmetic progression of primality radii of an integer $n$ as $n$ tends to infinity is unbounded? | |
| Nov 25, 2019 at 22:01 | comment | added | Wojowu | This only proves that in the sequence of primality radii of $n$ the lengths of arithmetic progressions are bounded, no? How do you conclude there are finitely many such numbers? | |
| Nov 25, 2019 at 21:59 | history | edited | Sylvain JULIEN | CC BY-SA 4.0 |
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| Nov 25, 2019 at 21:52 | history | edited | Sylvain JULIEN | CC BY-SA 4.0 |
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| Nov 25, 2019 at 21:45 | history | edited | Sylvain JULIEN | CC BY-SA 4.0 |
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| Nov 25, 2019 at 21:33 | history | edited | Sylvain JULIEN | CC BY-SA 4.0 |
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| Nov 25, 2019 at 21:20 | history | answered | Sylvain JULIEN | CC BY-SA 4.0 |