Probabilistic Proofs of Some Generalized Mertens' Formulas Via Generalized Dickman Distributions

Ross G. Pinsky

The classical Mertens' formula states that ${\prod }_{p\le N}(1-\frac{1}{p}{)}^{-1}\sim e^{\gamma }\log N,$ where the product is over all primes $p$ less than or equal to $N$, and $\gamma$ is the…