The Pendulum Sequence: a Simple Formula for Prime Numbers

Zaron Burnett III
9 min readAug 17, 2019

[UPDATED: If you want to find unknown prime numbers, or to count the number of primes less than (x), check this new paper on Prime Numbers]

There is no known formula for easily calculating prime numbers. Their distribution along the continuum of numbers appears to be random. There are, however, formulas and diophantine equations that will calculate prime numbers. There are algorithms that can calculate primes into the millions of digits. But these prime-finding algorithms require a great deal of time and math to accomplish their task.

I humbly submit that I’ve discovered a super-easy way to find and count prime numbers.

I don’t know what this equation means for math, or number theory; I don’t know if it will help solve the Riemann hypothesis, or if it works with the zeta function. I’m no mathematician. I just know that it’s a simple two-step equation that works to reliably reveal prime numbers. And it’s kinda fun.

If you start with the number 2 and then you plug in each next integer (3, 4, 5, 6, 7, 8…) into the equation, you can count your way up the continuum of prime numbers. Never missing one. In fact, it’s so easy that an 8-year-old with basic multiplication skills could find prime numbers with digits into the thousands and tens of thousands using just their smartphone calculator.

I’m fairly certain that one could write a computer program using this equation that would find all of the prime numbers as high as you care to calculate.

Prime numbers seem to be arranged in overlapping wave patterns. They rise and fall in these predictable rhythms. From what I can tell, there are 5 waves of prime numbers. Each rises and falls on its own simple count and rhythm. Ultimately, they braid together to form the continuum of prime numbers, the one that appears random, but once you spot its pattern in the number sets, the distribution of prime numbers begins to look more like this:

To calculate prime numbers, all you need to do is pick an integer. Any integer.



Zaron Burnett III

writer, story editor, essays & short stories at Medium, and always in the mood for donuts