# Inspried by Satyajit Mohanty

Let $$S$$ be the set of numbers less than $$5$$ billions and can be expressed in the form $$n^2+5n+23$$, where $$n$$ is a positive integer.

Let $$N$$ be the smallest prime number that divides for some elements of $$S$$.

Let $$p$$ be the number of elements of $$S$$ that are prime.

Let $$q$$ be the number of elements of $$S$$ that are divisible by $$N$$ .

Find $$N+p+q$$.

×