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Two Conjectures and their Proof through a Reduction to an Analogous Theorem

Author:

Nieves Rivas, Rodolfo A.

Category:

Essays

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

May 27, 2021

Downloads:

55

Keywords:

Polignac conjecture, Reduction, Analogous, theorem

Abstract:

Since Euclid proved the infinity of prime numbers [3] and the concern of all mathematicians arose to unravel the mystery that contains the prime numbers, which are called atoms of mathematics, one of the first problems proposed 2.300 years ago by Euclid which deals with the infinity of the twin prime numbers [1], which is still unsolvable. Then Alphonse de Polignac proposes his generalization, called the Polignac conjecture and in mathematical jargon known as the determination and proof of the prime numbers Ktwins, a problem that is taken up by Landau at the mathematics congress in 1912 in Cambridge, being known, from this date, as the problems of Landau. In this short article an analogous theorem of Polignac's conjecture is presented, thus achieving a reduction. Then the referred analogous theorem is proved, thus achieving the proof of this elusive conjecture, concluding that the twin prime conjecture is really a corollary of the analogous theorem, obtaining the proof of both conjectures.

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