A Wheel Through the Primes: A Concrete Tour of Analytic Number Theory (THE PRIMES TRILOGY)

Every road through the primes begins at the wheel.

Modulo 210 = 2·3·5·7, the integers fall into a fixed pattern: forty-eight residues coprime to the wheel, and the primes — with the stubborn subprimes among them — hiding in those lanes. A Wheel Through the Primes takes that single organizing idea and builds the concrete machinery of analytic number theory out of it: the sieve, the survivors, the Euler product that turns a counting problem into a function, and the first clear sight of the three walls every later road will run into.

The stance is plain throughout: real mathematics credited by name, metaphor kept distinct from mechanism, and the longer computations reproduced by deterministic Python you can run rather than take on faith.

The first book in the Primes Trilogy — the foundation the other two are built on.

John Maggio is an independent researcher and the co-founder of Advanced Fiber, Inc., a fiber optic systems firm handling splicing, testing, design, engineering, and troubleshooting. He writes on analytic number theory and the prime numbers, and The Primes Trilogy is his concrete, computation-checked tour of the Riemann Hypothesis and the mathematics built around it. The trilogy is published under his Efficient Intelligence, LLC imprint.