MathNet 2021 — Part 07 Question 19

For every positive integer $n$, let $f(n)$ be the smallest positive integer such that $f(n)$ is prime to $n$ and $f(n) + 1$ is prime to $n + 1$. How many different integers will appear in $\{f(1), f(2), \dots, f(10^{10})\}$?