Timeline for Remainder-balancedness of primes
Current License: CC BY-SA 4.0
12 events
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| Jan 21, 2023 at 11:03 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 21, 2023 at 11:03 | comment | added | Dominic van der Zypen | Thanks @WlodAA - will reformulate! | |
| Jan 21, 2023 at 10:28 | comment | added | Wlod AA | The last sentence before Question seems to be messed up (just in case, you could fix it perhaps). Anyway, this sounds as the weak version of Dirichlet Theorem (if I managed to parse your formulation well enoiugh). | |
| Jan 21, 2023 at 7:51 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 15, 2023 at 21:44 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 15, 2023 at 12:34 | comment | added | Dominic van der Zypen | @MartinSleziak Thank you - apologies for my sloppiness | |
| Jan 15, 2023 at 12:21 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 15, 2023 at 12:18 | comment | added | Dominic van der Zypen | Will correct the mistakes -- apologies for this bad question. | |
| Jan 15, 2023 at 12:12 | comment | added | Wojowu | I think you forgot to make your definition of remainder-balanced actually depend on $S$. If you meant $\mu^+(r_n^{-1}(\{a\})\cap S)$ in the definition, then the result is trivially true as primes, and all their subsets, have upper density $0$. If you meant to use relative density, the result is trivially false, as Martin points out. A corrected version is given by PNT in APs | |
| Jan 15, 2023 at 12:12 | comment | added | Martin Sleziak | BTW is "$\mu^+\big(r_n^{-1}(\{a\}\big)$" (with the right bracket missing) suppose to be "$\mu^+\big(r_n^{-1}(\{a\}\cap S)\big)$"? (I see that Wojowu was faster than me - I was looking for appropriate link concerning the same result.) | |
| Jan 15, 2023 at 12:06 | comment | added | Martin Sleziak | Maybe I misunderstood something, but it seems that $4\notin RB(P)$, since the only prime belonging to $4\mathbb N+2$ is two. And you can use basically the same argument for any integer which is not a prime. | |
| Jan 15, 2023 at 11:54 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |