The Prime Numbers’ Rhythm

Pateo TV, Ep. 41

In 2010, all-round researcher Johan Oldenkamp discovered the rhythm in the series of prime numbers. Even though he already tried to explain this Prime Numbers’ Rhythm as good as he could back then, not everyone was able to understand his explanation, and some even disliked it. That is why Johan made this 41st episode of Pateo TV, so that his improved explanation might enable more people to understand and enjoy this fascinating Prime Numbers’ Rhythm:

Related Post

• [link] Video Presentation on The Prime Rhythm of Oldenkamp

 

The logic of the Prime Rhythm becomes clear when we realize that a full circle equals to 2𝜋 radians (where 1 radian is the angle subtended by a portion of the circumference equal in length to the radius). Rounded to a ratio of integers, the first approximation of 2𝜋 is 6/1. That is why the Prime Rhythm plots all integers in 6/1 (= 6) consecutive directions. The prime numbers are in only 2 of these 6 directions, as shown in the Prime Rhythm. This number of 2 (prime directions) can also be calculated by Euler’s totient function.

A more accurate approximation of 2𝜋 is 44/7. When all positive integers are plotted in these 44 directions, the primes occur in 20 directions. An even more accurate approximation of 2𝜋 is 710/113. When all positive integers are plotted in these 710 directions, the primes occur in 280 directions. More on this is presented in a clear video on Dirichlet’s theorem.

In the fraction series of both 7 and 113, there is a repeating pattern, as shown in the video embedded below.