A proper vertex colouring of a graph $G$ is a colouring of the vertices in $G$ in such a way that two vertices get different colours if they are adjacent. The minimum number of colours required for proper vertex colouring of $G$ is called the chromatic number of $G$. Then what is the chromatic number of the cycle graph on 149 vertices?

Which of the following statement(s) is(are) true? If $n$ is odd prime number then $2^{n-1} \text{ mod } n =1$ If $2^{n-1} \text{ mod } n =1$ for a number $n$ then $n$ is prime