AlexKontorovich/PrimeNumberTheoremAnd
Source indexedtheorem · leanprover/lean4:v4.32.0
Goldbach.ramare_saouter_odd_goldbach
PrimeNumberTheoremAnd.IEANTN.Goldbach · PrimeNumberTheoremAnd/IEANTN/Goldbach.lean:157 to 173
Mathematical statement
Exact Lean statement
@[blueprint
"ramare-saouter-odd-goldbach"
(title := "Ramaré and Saouter's verification of odd Goldbach")
(statement := /-- \cite[Corollary 1]{ramare-saouter}
The odd Goldbach conjecture is verified up to $1.13256 \times 10^{22}$. -/)
(proof := /-- Combine Proposition \ref{richstein-even-goldbach},
Proposition \ref{even-to-odd-goldbach-triv}, and Theorem \ref{thm:ramare-saouter2003}. -/)
(latexEnv := "proposition")
(discussion := 962)]
theorem ramare_saouter_odd_goldbach : odd_conjecture 11325599999999886744004Complete declaration
Lean source
Full Lean sourceLean 4
@[blueprint "ramare-saouter-odd-goldbach" (title := "Ramaré and Saouter's verification of odd Goldbach") (statement := /-- \cite[Corollary 1]{ramare-saouter} The odd Goldbach conjecture is verified up to $1.13256 \times 10^{22}$. -/) (proof := /-- Combine Proposition \ref{richstein-even-goldbach}, Proposition \ref{even-to-odd-goldbach-triv}, and Theorem \ref{thm:ramare-saouter2003}. -/) (latexEnv := "proposition") (discussion := 962)]theorem ramare_saouter_odd_goldbach : odd_conjecture 11325599999999886744004 := by have h1 := even_to_odd_goldbach 10726905042 (4 * 10 ^ 14) 28314000 (fun x hx => RamareSaouter2003.has_prime_in_interval x (by norm_cast : (x : ℝ) > 10726905041)) richstein_goldbach have h2 := odd_conjecture_mono (4 * 10 ^ 14 + 3) 10726905046 (even_to_odd_goldbach_triv _ richstein_goldbach) norm_num at * exact h1 h2