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 2020-12-29, 14:04 #1 gnostique   Dec 2020 716 Posts 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: prime sequences and distributions Distributions of twin prime sequences were discussed earlier in: twin prime distributions
 2020-12-31, 15:29 #2 mart_r     Dec 2008 you know...around... 10101011012 Posts 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.
 2021-01-11, 19:17 #3 Bobby Jacobs     May 2018 3558 Posts Interesting article. Twin primes are full of great patterns. They are very cool.
2021-03-06, 13:46   #4
gnostique

Dec 2020

7 Posts

Quote:
 Originally Posted by mart_r 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.

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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