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22 - The Series of Primes (iii)

Table of contents

  • 22.1 The Functions \vartheta(x) and \psi(x)
  • 22.2 Proof that \vartheta(x) and \psi(x) are of Order x
  • 22.3 Bertrand’s Postulate and a “Formula” for Primes
  • 22.4 Proof of Theorems 7 and 9
  • 22.5 Two Formal Transformations
  • 22.6 An Important Sum
  • 22.7 The Sum \sum p^{-1} and the Product \prod (1 - p^{-1})
  • 22.8 Merten’s Theorem
  • 22.9 Proof of Theorems 323 and 328
  • 22.10 The Number of Prime Factors of n
  • 22.11 The Normal Order of w(n) and G(n)
  • 22.12 A Note on Round Numbers
  • 22.13 The Normal Order of d(n)
  • 22.14 Selberg’s Theorem
  • 22.15 The Functions R(x) and V(\xi)
  • 22.16 Completion of the Proof of Theorems 434, 6 and 8
  • 22.17 Proof of Theorem 355
  • 22.18 Products of k Prime Factors
  • 22.19 Primes in an Interval
  • 22.20 A Conjecture About the Distribution of Prime Pairs p, p + 2

22.1 The Functions ϑ(x) and ψ(x)

22.2 Proof that ϑ(x) and ψ(x) are of Order x

22.3 Bertrand’s Postulate and a “Formula” for Primes

22.4 Proof of Theorems 7 and 9

22.5 Two Formal Transformations

22.6 An Important Sum

22.7 The Sum ∑p−1 and the Product ∏(1−p−1)

22.8 Merten’s Theorem

22.9 Proof of Theorems 323 and 328

22.10 The Number of Prime Factors of n

22.11 The Normal Order of w(n) and G(n)

22.12 A Note on Round Numbers

22.13 The Normal Order of d(n)

22.14 Selberg’s Theorem

22.15 The Functions R(x) and V(ξ)

22.16 Completion of the Proof of Theorems 434, 6 and 8

22.17 Proof of Theorem 355

22.18 Products of k Prime Factors

22.19 Primes in an Interval

22.20 A Conjecture About the Distribution of Prime Pairs p,p+2


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