Physics, mathematics, and technology

2019 Issue №2

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About one way of determination of prime numbers



The method of finding prime numbers without computer calculation is shown. Subsets P1 = {6k1 – 1}, P2 = {6k2 + 1}, Q1 = {6j1 – 1}, Q2 = {6j2 + 1} are considered, where P1 È P2 are all prime numbers p ≥ 5; Qi are all odd composite numbers of such form. Subsets Ai = {ki}, Bi = {ji} (i = 1, 2) are investigated. It is proved that Bi by exploit sequences of natural numbers are lastly defined for ji £ a ⋲ N. Numbers ki are omitted natural numbers in Bi as Ai = N\Bi. For ki £ 200 all numbers of the sets Ai (and therefore all such prime numbers of the sets Pi) are defined.


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