A new way to locate and prove primality. No trial division, no sieves... just equations.

The Prime Wave: A New Way to Understand Primes

For thousands of years, primes have been treated as mysteries—special numbers that resist being divided. We’ve built countless algorithms to find them, test them, and use them (especially in cryptography), but we’ve never really understood why they appear where they do.

This project started from a different angle. Instead of thinking of numbers as static objects in a list, we modeled them as fields—waveforms spread over a circle. Every number bends that circle a little, depending on its internal structure.

A prime? It doesn’t bend the circle at all. The field stays perfectly flat.

That’s the idea: primes don’t show up because they can’t be divided. They show up because nothing inside them resonates. They're moments of silence in a noisy system.

Using Python, we built a way to simulate this. We don’t guess whether a number is prime—we watch to see if the field stays silent. If it does, we mark it.

But the deeper insight came later: if you watch how one prime ends the noise of everything before it, you can invert that wave and watch it move forward. Where the field goes silent again? That’s your next prime.

No sieves. No trial division. Just conservation, symmetry, and cancellation.

This is a tool. You can use it yourself, step by step, and see what happens.
These posts are more accessible to regular readers. The math is far more easy to follow and we aren't tracking ungrounded imaginary pivots in the Zeta Function. 🤣

https://qmichaellewis.blogspot.com/2025/04/the-prime-frequency-rethinking.html

https://qmichaellewis.blogspot.com/2025/04/computing-prime-wave-complete-guide-for.html

Here's the walk-through, the full theory, and the Python for those of us who don't know how to formulate our own Lagrangian:

https://qmichaellewis.blogspot.com/2025/04/the-prime-wave-on-curvature-of-integer.html

https://qmichaellewis.blogspot.com/2025/04/hacking-primes-every-conserved-quantity.html

Enjoy and...

Even though the math checks out... this still has to be proven by real people who have actually paid good money know how to do math and physics before you can use this. My training and expertise is not sufficient enough but regardless, I am using this to create the next class of computers so my concerns about academic rigor and peer review are nonexistent.

Please don't go running around thinking someone figured out Prime numbers... even if I'm right and I AM, academia needs to prove it to you, not some uneducated person. Real science still has to make and claim this discovery.

Well, academia needs to prove it before YOU can use it or believe it but be patient. I intend to do some amazing things with it! Starting with an entirely new AI!