Question 146
There are 4037 light bulbs arranged in a row and numbered from 1 to 4037. Initially each bulb can be on or off. A move consists of choosing two bulbs numbered $a, b$ such that $a / b$ or $b / a$ is a prime number and changing the state of both. Prove that in a finite number of moves one can turn on all the bulbs from 1 to 2019, whatever the initial configuration.