Timeline for Partitioning an infinite sumset into primes and composites
Current License: CC BY-SA 4.0
Post Revisions
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2025 at 22:39 | comment | added | DimensionalBeing | @YemonChoi: initially was attempting to visualize it an infinite grid where we need to color entries based on their position relative to the diagonal. But then I discarded that viewpoint as it became too complicated. | |
| Jun 29, 2025 at 22:29 | comment | added | Yemon Choi | Is there any reason for introducing the notation $S_{ij}$? | |
| Jun 29, 2025 at 21:48 | comment | added | Joel Moreira | Also I expect the answer to be almost certainly yes, and it may even follow from the Tao-Ziegler argument if one is careful enough to keep track of the composite numbers in the Maynard sieve (which should be the easy part). | |
| Jun 29, 2025 at 21:38 | comment | added | Joel Moreira | As pointed out by mathworer21, Tao and Ziegler show that there are sequences $(a_i)$ and $(b_j)$ satisfying the first condition $a_i+b_j$ is prime whenever $i<j$. Since $a_i+b_j$ is either a prime or a composite for any $j\leq i$, using Ramsey's theorem one can extract subsequences $(c_i)$ of $(a_i)$ and $(d_j)$ of $(b_j)$ which either satisfy the second condition; or satisfy that $c_i+d_j$ is prime for every $i,j$. | |
| Jun 28, 2025 at 20:21 | comment | added | mathworker21 | This is of course relevant. | |
| Jun 28, 2025 at 19:48 | history | asked | DimensionalBeing | CC BY-SA 4.0 |