Existence of a Quadratic Polynomial, Which Represents Infinitely Many Prime Numbers: Bunyakovsky's Conjecture for Degree Greater than One and the 4th Landau Problem

EasyChair Preprint 8203, version 3

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).

Keyphrases: Bunyakovsky’s conjecture, Euler’s 6k + 1 theorem, Fermat’s theorem on sums of two squares, Landau’s problems, complete and subcomplete sequences, 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: Bunyakovsky's Conjecture for Degree Greater than One and the 4th Landau Problem},
  howpublished = {EasyChair Preprint 8203},
  year      = {EasyChair, 2023}}