Tuesday, June 05, 2018

Revisiting my discovery of some effect in the distribution of primes

I mentioned it in on this blog in February. At that time, I already had a preprint written, which since then has gone through a few updates. I think I am pretty close to a final version.

Its title is "Statistical Bias in the Distribution of Prime Pairs and Isolated Primes." You can read it at this preprint repository. The paper is rather simple. A high school student with a decent math background should be able to follow it and even verify its findings for herself (ladies first) or himself. All the data, the code for a free software package that was used for this research and, of course, all the reasoning (very simple, in fact) that led to this discovery are in there.

The effect is novel compared to similar effects known before (such as the Chebyshev bias) and also significantly larger, even by 1-2 orders of magnitude.

I will probably try to get this research published in one of those peer-reviewed journals, if I find time for that. Not to mention the patience to deal with the peers. Yep, that's the people who have overlooked this effect, pretty large too, for whole generations. Some peers.

Thanks to the Interweb, the progress in science and mathematics is being communicated in real time and no stinking peer-review is needed for that. And it's really not a peer-review that ultimately decides if something is important and becomes a permanent part of mathematical or scientific knowledge. Important things once discovered usually remain part of such knowledge forever.