IKBFU's Vestnik

2019 Issue №02

Back to the list Download an article

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.


1.  Боро В., Цагир Д., Рольфс Ю. и др. Живые числа. М., 1985.

2.  Малаховский В. С. Числа знакомые и незнакомые. Калининград, 2004.

3.  Малаховский В. С. Удивительные свойства двух первых простых чисел // Диф. геом. многообр. фигур : межвуз. темат. сб. науч. тр. Калининград, 2017. Вып. 48. С. 69—73.