Consider the product P=∏p≤x(1−1p)−1P = \prod_{p \leq x} (1 - \frac{1}{p})^{-1}P=∏p≤x(1−p1)−1. As x→∞x \to \inftyx→∞, this product behaves like:
lnx\ln xlnx
eγlnxe^\gamma \ln xeγlnx
π(x)\pi(x)π(x)
1/lnx1/\ln x1/lnx