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Article . 2023 . Peer-reviewed
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Preprint . 2023
License: CC BY
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The Hyperbolic Sieve of Prime Numbers

Authors: Kusniec, Charles;

The Hyperbolic Sieve of Prime Numbers

Abstract

We start this study producing the HL - Hyperbolic Lattice Grid in the form of HL[x,y]=x*y. Then we show that the SMT – Square Multiplication Table is the result of the integer coordinates of the HL - Hyperbolic Lattice Grid in the form of HL[x,y]=x*y, in the first quadrant. From the SMT we define the SMTSP – Square Multiplication Table Sieve of Primes. Then we show the SMT covered by the quadratic sequences in the form of x=y(y±b). Then, we expand the SMT to the FMT - Full Multiplication Table. Because of the FMT, we define all integers in terms of the Pairs of Complementary Divisors (x;y). We make a disambiguation between factors and divisors. From these properties, we created the TMTSP - Triangular Multiplication Table Sieve of Prime Numbers. The Pairs of Complementary Divisors (x;y) of integers are exactly the pairs of integer coordinates (x,y) of the Cartesian points of TMTSP in the XY-plane. From the TMT we define the TMTSP – Triangular Multiplication Table Sieve of Primes. The multiplication table proves that all integers must be classified as primes or composites, no exception. There is an equivalence (or isomorphism) between the Hyperbolic Sieve of Primes with the Parabolic Sieve of Primes. Both produce identical results.

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Keywords

Sieve of prime numbers, pair of complementary divisors, hyperbolic lattice grid

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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