Overview

This book offers several proofs that deal with prime numbers. A proof by contradiction of Goldbach's binary conjecture that every even natural number greater than two (2) can be expressed as the sum of two (2) primes is given. A proof of Goldbach's ternary conjecture that all natural numbers greater than five (5) are the sum of three (3) primes via the binary proof is presented. A proof by construction (utilizing the proof of the binary conjecture) of the twin prime conjecture is offered. A proof of the Riemann hypothesis by deduction is presented. A proof that any prime greater than three (3) is the mean of two other primes is presented. A proof is offered that any even number greater than fourteen (14) satisfies Goldbach's binary conjecture in a plurality of ways. Two entangled formulas that generate all the primes beyond the second prime (P2 = 3) are developed and summarized. Proofs of Andrica's, Legendre's and Brocard's conjectures are offered.

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9781448621255

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Shelton W. Riggs, Jr. earned undergraduate (University of Texas) and graduate (Vanderbilt) degrees in both Physics and Mathematics. Professionally, he has consulted as both a hardware and software design engineer to numerous Fortune 500 companies for a wide range of scientific applications. He helped solve several scientific problems for US Army, Air Force and Navy. Other interests include theoretical physics including quantum mechanics, relativistic mechanics and theoretical mathematics (especially the mystery of prime numbers). Hobbies include dancing, karaoke, juggling, playing keyboards, writing songs, and writing poetry.

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