Number Theory


Generalized Conjecture on the Distribution of Prime Numbers

Authors: Réjean Labrie

Abstract: Let N, n and k be integers larger than 1. Then for all N there exists a minimum threshold k such that for n>=N, if we cut the sequence of consecutive integers from 1 to n*(n+k) into n+k slices of length n, we always find at least a prime number in each slice. It follows that π(n*(n+k)) > π(n*(n+k-1)) > π(n*(n+k-2)) > π(n*(n+k-3))> ...> π(2n)> π(n) where π(n) is the quantity of prime numbers smaller than or equal to n.

Comments: 6 Pages.

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Submission history

[v1] 2018-02-13 22:51:29
[v2] 2018-02-14 09:08:19

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