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:

http://lesswrong.com/r/discussion/lw/pbe/open_thread_august_7_august_13_2017/dw37

Spotted by a machine

If some number N, in the binary representation has 3 0’s and 13 1’s, then N+1 is NEVER a prime number.

This is about sigma 6 event.

 

ADDED:

If some number N, in the binary representation has 2 0’s and 14 1’s, then N itself  is NEVER a prime number.

This is also about sigma 6 event.