# Mertens' asymptotic formula for $\prod \left(1-p^{-1}\right)$ without constant

I've heard that there is an easy way to derive the asymptotic $$\prod_{p\le x} \left(1-\frac{1}{p}\right) \sim \frac{c}{\log(x)}$$ if one isn't interested in deriving $c=e^{-\gamma}$. I don't see how to do this, however. Does anyone here know where I could find a simple proof of this statement or even write down a proof for me?

I'm quite new to number theory, so if you only assumed minimal background, that would be very helpful. Thanks for your help!

• Perhaps that this thread will help. – Raymond Manzoni Oct 25 '12 at 22:08
• @RaymondManzoni: Thank you for the link! – Sam Oct 26 '12 at 10:36

See pages 21-22 of Gérald Tenenbaum and Michel Mendès France, The Prime Numbers and Their Distribution. I found that by typing $$\rm Mertens\ formula$$ into the web. Many other possibly useful references came up, as well; for example, the discussion starting on page 88 of Hildebrand's notes.
• Cheers! ${}{}{}{}$ – Sam Oct 25 '12 at 22:20