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-   -   Prime sequences and gaps: conditions and heuristics (https://www.mersenneforum.org/showthread.php?t=26350)

gnostique 2020-12-29 14:04

Prime sequences and gaps: conditions and heuristics
 
Maybe this material can be of interest to researchers, both theoretical and numerical in prime gap distributions. It provides necessary and sufficient conditions for quadruplet prime sequences, no-prime sequences and some cases in Polignac's conjecture:
[URL="https://www.cambridge.org/engage/coe/article-details/5fd8c7050bf9660018a23748"]prime sequences and distributions[/URL]


Distributions of twin prime sequences were discussed earlier in:
[URL="https://www.cambridge.org/engage/coe/article-details/5fce49501ad9a000182972f3"]twin prime distributions[/URL]

mart_r 2020-12-31 15:29

As the layman I am, I'm having a surprisingly difficult time understanding this.
The paper looks well written, but it seems to merely provide a more complicated way of stating what is already known about sets of odd coprimes, though I'll be gladly proven wrong in this regard.

Bobby Jacobs 2021-01-11 19:17

Interesting article. Twin primes are full of great patterns. They are very cool.

gnostique 2021-03-06 13:46

[QUOTE=mart_r;567844]As the layman I am, I'm having a surprisingly difficult time understanding this.
The paper looks well written, but it seems to merely provide a more complicated way of stating what is already known about sets of odd coprimes, though I'll be gladly proven wrong in this regard.[/QUOTE]


The approach provides a description of the mechanism driving the distribution of twin primes, and importantly, other types of prime sequences as quadruplets, some Polignac's patterns and possibly others. It allows to obtain numerically verifiable bounds on the distributions of twins and other sequences. Developing it further may allow to advance toward formal proof of the bounds that could help to stand some long standing problems.


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