The sequence of the primes is something of a mystery in number theory‚ if not in all of mathematics. Hardly any topic has ever fascinated mathe¬maticians more. Euler once said‚ “Mathematicians have tried in vain‚ to this day‚ to discover some order in the sequence of prime numbers‚ and we have reason to believe that it is a mystery into which the mind will never penetrate”. One key question has always been: Does there exist a single‚ overarching organisational principle that accounts for why any prime follows another prime as the next largest prime in the prime sequence?
A primary aim of this book is to show that such overarching and comprehensive principles do exist and govern the entire prime sequence. To unlock these secrets of harmony, for the enthusiastic reader, it is not necessary to dive too deep into mathematics‚ but to unveil structures of organisation from different points of view.
The Secret Harmony of Primes was written in 2012-2015 and represents a collection of the author's work in prime number theory throughout the last decades‚ woven into a comprehensible storyline.
|Product dimensions:||5.00(w) x 7.99(h) x 0.24(d)|
About the Author
Table of Contents(1) Fundamentals: 1‚ 2‚ 3‚ 4‚... N is not a number//W(e)aving N//2‚ 3‚ 5‚ 7‚... p is a prime//The fundamental theorem of arithmetic//The log-canonical form//(2)Structures of Harmony: The prime exponent theorem//The prime modular vectors//Using the Euler Gamma function//The trivial relation to the sinc function//Back to the structure of elementary prime exponent vectors//(3)Secrets of Design: The curve family over the prime exponent vectors//Scaling in a metric space//(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 Z//(5) Zeta//The Recursive Sequence of the Primes//(6)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?