This problem was studied first by the founder of sieve theory, Brun himself, who proved this asymptotic.  For a fairly recent paper on this subject look at Andersson who gives more precise estimates for $u_n$.  The MO question Sequences with integral means is also closely related, and see also my answer there.  

Why does this sequence converges to $\pi$?
ActionController::RoutingError (No route matches [GET] "/google83362a7a0f381ff0.html"):


I see the above logs in production, how should I prevent it.
If user mistypes a URL, how should I re-direct to a common error page

