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 no. 8203

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.

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: Bunyakovsky's Conjecture for Degree Greater than One and the 4th Landau Problem},
  howpublished = {EasyChair Preprint no. 8203},

  year = {EasyChair, 2022}}