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Contents

PREFACE

CHAPTER 1

Fundamentals

is not a number

W(e)aving

is a prime

The fundamental theorem of arithmetic

The log-canonical form

CHAPTER 2

Structures of Harmony

The prime exponent theorem

The prime power modulo functions

(a) The relation to the Euler Gamma function

(b) The trivial relation to the function

The elementary prime exponent functions

CHAPTER 3

Secrets of Design

The curve family over the prime exponent vectors

Scaling in a metric space

CHAPTER 4

The Spectrum

The reconstruction of the log-canonical form

Certainty versus uncertainty

The orbits

The spectrum of natural numbers

The log-canonical form for

CHAPTER 5

Zeta

CHAPTER 6

The Recursive Sequence of the Primes

The implicit recursive sequence of the primes

On the Number of Primes Less Than a Given Magnitude

The implicit recursive sequence of the primes

The interference prime counting function

How fair are the prime number dice of Gauss?

NOTES

The Secret Harmony of Primes

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