Timeline for Expliciting the distance between consecutive Goldbach numbers assuming it's finite
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 14, 2015 at 21:05 | comment | added | GH from MO | Density one is an old result, about 75 years old. By more elaborate techniques it is even known that up to $x$ there are only $O(x^{2/3})$ exceptions to Goldbach's conjecture (Pintz, unpublished). Establishing the existence of $C$ or bounding it (assuming its existence) is another matter. But who knows, maybe more breakthroughs are around the corner. | |
| May 14, 2015 at 21:00 | comment | added | Sylvain JULIEN | I read somewhere (wikipedia?) that it has been proven that the set of Goldbach numbers has natural asymptotic density one, so maybe an explicit value for $C$ is attainable. | |
| May 14, 2015 at 20:55 | comment | added | GH from MO | I think it would be a fantastic result if we could prove that the existence of $C$ implies a concrete value for $C$. This result is not in the literature, so it is fair to say that it is not possible to make $C$ explicit with current technology. Of course any new paper might change this opinion, e.g. Zhang and Maynard-Tao also used existing technologies, but noone believed a few years ago that their results were within reach. | |
| May 14, 2015 at 20:34 | history | asked | Sylvain JULIEN | CC BY-SA 3.0 |