Three asymptotic estimates on primes due to Mertens (1874): (1) Σ_{p ≤ n} (ln p)/p = ln n + O(1); (2) Σ_{p ≤ n} 1/p = ln ln n + M + o(1), where M ≈ 0.2614… is the Meissel–Mertens constant; (3) Π_{p ≤ n} (1 − 1/p) ~ e^(−γ) / ln n. Sharpens…
Three asymptotic estimates on primes due to Mertens (1874): (1) Σ_{p ≤ n} (ln p)/p = ln n + O(1); (2) Σ_{p ≤ n} 1/p = ln ln n + M + o(1), where M ≈ 0.2614… is the Meissel–Mertens constant; (3) Π_{p ≤ n} (1 − 1/p) ~ e^(−γ) / ln n. Sharpens…