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- W2749205923 abstract "The article focuses on methods defining and distributing the composite numbers, prime numbers, twins of prime numbers and composite numbers of twins that do not have divisors 2 and 3 in N , based on the set of numbers of type Θ = {6 k ± 1 / kN } where N is the set of all natural numbers, which is a semigroup with respect to multiplication. The calculation the exact quantity of primes in a given interval is given. A method for obtaining prime numbers p ≥ 5 by their ordinal numbers in a set of primes p ≥ 5 is proposed, as well as a new algorithm for finding and distributing prime numbers on the basis of the closeness of the set Θ. The article shows that any composite number n Θ is representable as products (6 x ± 1) (6 y ± 1), where x, yN are the natural solutions of one of the four Diophantine equations P ( x , y , λ) = 0 : 6 × xy ± x ± y - λ = 0. It has been proved that if there is a parameter λ of twins of prime numbers, then none of the Diophantine P ( x , y , λ) = 0 equations has any solutions. A new universal, deterministic, polynomial and independent verification test is provided for the simplicity of the numbers of a species 6 × k ± 1. Algorithms of distributions of parameters of twins of prime numbers and parameters composite numbers of twins are given, they are not divisible by 2 and 3, and variants of proofs for their infinite number are given." @default.
- W2749205923 created "2017-08-31" @default.
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- W2749205923 date "2017-07-25" @default.
- W2749205923 modified "2023-09-27" @default.
- W2749205923 title "DISTRIBUTION OF PRIME AND COMPOSITE NUMBERS AND THEIR ALGORHYTHMIC APPENDICES" @default.
- W2749205923 doi "https://doi.org/10.24143/2072-9502-2017-3-48-64" @default.
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