Number Theory

    

Isolating the Prime Numbers

Authors: Adrian M. Stokes

Prime numbers greater than 3 belong to the number sequences 6n ± 1 wheren ≥ 1. These sequences also include the composites that are not divisible by 2 and/or3 and therefore their factors must also be of the form 6n ± 1. This allows all of the6n±1 composites to be equivalently written in the form of factors (6n1±1)(6n2±1),where n1 and n2 ≥ 1, creating three sub-sequences that exclude prime numbers.Finding and isolating the prime numbers can be achieved by selecting a numberrange and creating a set of 6n ± 1 numbers for that range before subtracting thesubsets (6n1 ± 1)(6n2 ± 1) to isolate and identify all the primes in the set.

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[v1] 2024-02-29 23:10:30

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