How To Find Unknown Prime Numbers and Count the Number of Primes Less than (X)

In a famous 1975 lecture, mathematician Don Zagier told a gathered crowd of math lovers:

“There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision”

Quite humbly, I submit that I’ve discovered an underlying dynamic that explains these laws and that what I found makes sense of the contradictory dualistic behavior of prime numbers.

This whole paper could be just a few equations and examples, but I’d like this to be intelligible for anyone curious to understand the mystery of the primes. So this presentation is intended to be accessible to the general reader.

It’s often said: bold claims require solid evidence. Let’s break out the…