I developed Prime Spy using Claude and Gemini because I have always felt that clues to the distribution of primes could be found among the figurate numbers, and perhaps more risque, that there could be some sort of squeeze theorem that could predict where primes exist between some formula. Not being a mathematician, it’s totally absurd that I should be making guesses at all. Least of all for one of the most important questions in mathematics, one for which our most talented mathematicians have been working on for more than 2,000 years. Still, I wanted to gain some insight into primes, and built this Prime Spy to meet that goal.
Prime Spy is a browser-based tool for looking at the whole numbers and, in particular, at the primes hiding among them. Rather than presenting primes as a list, it plots the integers as points you can arrange in several geometric layouts, overlay with well-known number sequences, drive with your own mathematical formulas, and inspect one at a time. The goal is exploration: to make the patterns that mathematicians describe in symbols something you can see, pan across, and zoom into.
This guide explains what the application is for, walks through every feature, and offers a set of short recipes for producing specific, revealing pictures. It is written to be read start to finish by a newcomer, or dipped into as a reference by someone who already has the app open.
You need no special background beyond secondary-school arithmetic. If you know what a prime number is, you can use every feature in the application. Readers who enjoy number theory will find familiar objects — the prime-counting function, figurate numbers, the Prime Number Theorem — presented visually and interactively. Educators may find the layouts useful for demonstrations.
Play with it here: https://xenius.org/PrimeSpy/
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