Function approximating this product Is there any function approximating, for large values of $p$, the quotient between the product of all primes and the product of all primes $-1$?
Basically: $2/1 \cdot 3/2 \cdot 5/4 \cdot 7/6 \cdot 11/10 \cdots $
Can that be approximated, for large values of $p$, with some known function?
Thank you very much.

You are asking for an approximation of  $$\prod_{p\leq n} \frac{p}{p-1}$$
It is well known that  $\prod_{p\leq n} \frac{p}{p-1} \simeq lnn$.
For more details and to learn how Euler used this fact to prove something really interesting see here
