The prime number distribution was solved already. Not only did Agrawal publish his equation in 2002, my information was published in 2000.

Long story short, prime numbers are the 'open frame' which is a term used in bowling to declare the pegs left standing after a bowling ball hit some of them.

Prime numbers can be declared as 'virgin' numbers compared to the other numbers because nothing divisible happened to them; they are untouched.

Eratosthenes got really close to the ultimate outcome, but he did not find the last step: the link between all steps. There is no mystery left about the prime numbers.

There was yet a greater surprise waiting once the prime numbers are seen as fully predictable: the link pattern among all steps contains the required use of zero.

https://www.cantorsparadise.com/discovering-zero-among-the-prime-numbers-65a47cbf79ec

In this article, the steps are shown to find all prime numbers by linking all other numbers in a single pattern. The 'open frame' are the resulting remaining numbers, and they are all the prime numbers.

The find of zero among all this (zero is of course not a prime number) is most wonderful, more so than knowing all prime numbers, because it means that zero is not only part and parcel of the natural numbers, but that it can be functional. An actual function can be associated with zero that no other number can deliver. That is very insightful.

Many people think that zero can be seen as something singular, but that is not true. Only number 1 can be seen as singular (and this is not always the case). Zero is not singular. The universe is based on the same principles as the binary system. The decimal system is a secondary system.