Consider the Euler product ζ(s) = product_(k = 1)^∞ 1/(1 - 1/p_k^s), where ζ(s) is the Riemann zeta function and p_k is the kth prime. ζ(1) = ∞, but taking the finite product up to k = n, premultiplying by a factor 1/ln p_n, and letting n->∞ gives lim_(n->∞) 1/(ln p_n) product_(k = 1)^n 1/(1 - 1/p_k) | = | e^γ | = | 1.78107..., where γ is the Euler-Mascheroni constant. This amazing result is known as the Mertens theorem.
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