Number Theory

    

Sieving Primes from Composite Pairs Within Sets of 6n±1 Numbers

Authors: Adrian M. Stokes

The prime numbers ≥ 5 within a finite sequence of natural numbers can be found by calculating all of the values given by 6n±1 that fall within the sequence and subtracting the composites given by (6n_1±1)(6n_2±1), where n is a natural number. A test model for finding primes based on this method uses three reference sub-set multiplication tables to calculate composites and then matches these to the corresponding values in the sets {6n-1} and {6n+1}. The unmatched numbers are primes. Although this model provides a useful proof of concept, it is impractical at scale. A new method that replaces the sub-set tables with an equation to calculate 6n±1 composite pairs forms the basis of an improved model using sieve methodology.

Comments: 5 Pages.

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Submission history

[v1] 2024-08-11 21:06:58

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