**Author:**

Nieves Rivas, Rodolfo A.

**Sub-Category:**

Mathematics and Applied Mathematics

**Date Published:**

May 27, 2021

**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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