Existence of a Quadratic Polynomial, Which Represents Infinitely Many Prime Numbers

EasyChair Preprint no. 8203, version 4

Abstract

No single case of Bunyakovsky's conjecture for degree greater than one has been proved, although numerical evidence in higher degree is consistent with the conjecture. In this paper we overcome such misfortune (using Friedlander–Iwaniec theorem, Fermat’s theorem on sums of two squares and Brahmagupta–Fibonacci Identity, Bezout’s lemma and a connection to SL(2, Z) and Hyperbolic Prime Number Theorem).

Keyphrases: Bunyakovsky’s conjecture, complete and subcomplete sequences, Euler’s 6k + 1 theorem, Fermat’s theorem on sums of two squares, Landau’s problems, prime numbers, primes represented by polynomials, sieve theory

@Booklet{EasyChair:8203,
  author = {Valerii Sopin},
  title = {Existence of a Quadratic Polynomial, Which Represents Infinitely Many Prime Numbers},
  howpublished = {EasyChair Preprint no. 8203},

  year = {EasyChair, 2023}}