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'Sensational' Proof Delivers New Insights into Prime Numbers
- KolenCh 2y agoDup: 'Sensational' Proof Delivers New Insights into Prime Numbers https://news.ycombinator.com/item?id=40968164 https://news.ycombinator.com/item?id=40968164
- klysm 2y agoI'm curious what the specific bounds were before and after this proof.
- cvcount 2y agoPerhaps this will help? https://mathstodon.xyz/@tao/112557249982780815 https://mathstodon.xyz/@tao/112557249982780815
- ano-ther 2y agoThis is really well explained. The video helped me to finally understand the connection between zeta function and prime distribution.
- neoneye2 2y agoAs a hobby project, I did investigate the distribution of prime numbers. The primes are somewhat evenly spaced with this transformation, I'm the author of it. A342730: a(n) = floor((frac(e * n) + 1) * prime(n+1)). https://oeis.org/A342730/a342730.png https://oeis.org/A342730/a342730.png Instead of e, I have tried other constants such as pi, but it doesn't look as good. I guess there is another constant that makes the distribution look even nicer.
- madcaptenor 2y agoI don't think this is anything special about primes or e - if you replace prime(n+1) with just (n+1) itself you get the same sort of patterns. But it is something to do with approximations of irrationals by rationals - you might want to look into continued fractions. Try replacing e with a rational number a/b (say 8/3 or 11/4); then you get b horizontal-ish lines, corresponding to the different remainders of n when divided by b. So the pattern you get with pi isn't "as good" because pi is famously close to 22/7.
- wizzwizz4 2y agoIn that case, you might get the best results with Liouville numbers.