prime numbers

Prime Towers Problem

There are 1 billion towers in line on a plane. The distance between the n-th and the (n+1)-th tower is 1 kilometer. The first is 2 kilometers tall, the second is 3 kilometers tall, the next one is 5 … and the n-th is the n-th prime number kilometers high.

From which tower’s top, the maximal number of tower tops are visible? In both directions.

A discussion is anticipated there: