Vinogradov's three primes theorem and almost all binary Goldbach, after Heath-Brown 1985, with the Siegel-Walfisz theorem
A sorry-free Lean 4 proof of the main results of D. R. Heath-Brown, The ternary Goldbach problem, Rev. Mat. Iberoam. 1 (1985): the Siegel-Walfisz theorem in the form the paper quotes as (1.1), proved from a zero-free region for Dirichlet L-functions and Siegel's theorem; Theorem 1, sum over 2x < m <= 3x of |N2(m) - x S(m)| << x^2 (log x)^{-C}; Corollary 1 and the van der Corput, Chudakov, Estermann theorem that at most O(X (log X)^{-A}) even numbers up to X are not sums of two primes, and density zero; Corollary 2, Vinogradov's theorem that every sufficiently large odd number is a sum of…
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