OMM 2014 Problem 1

Each of the integers from 1 to 4027 has been colored either green or red. Changing the color of a number is making it red if it was green and making it green if it was red. Two positive integers $m$ and $n$ are said to be cuates if either $\frac{m}{n}$ or $\frac{n}{m}$ is a prime number. A step consists in choosing two numbers that are cuates and changing the color of each of them. Show it is possible to apply a sequence of steps such that every integer from 1 to 2014 is green.