Problem 851

Erdős Problem #851: declared status 'proved'. Formalized: yes. Let $\epsilon>0$. Is there some $r\ll_\epsilon 1$ such that the density of integers of the form $2^k+n$, where $k\geq 0$ and $n$ has at most $r$ prime divisors, is at least $1-\epsilon$? Prize: no. Tags: number theory.