It is trivial that there are no polynomial function $P$ with integer coefficients that has the property $P(n)=p_n$ where $p_n$ is the $n$th prime.While it is true that can always construct a smooth function with this property.But what if we require the function to be real analytic ? Does there exists an analytic function $P$ that has the property $P(n)=p_n$ and its taylor series has integer coefficients?
