Introduction to Number Theory: Fascinating Facts and Conjectures about Primes and Other Special Numbers

I discuss here off-the-beaten-path beautiful, even spectacular results from number theory: not just about prime numbers, but also about related problems such as integers that are sum of two squares. The connection between these numbers and prime numbers will appear later in this article. A few important unsolved mathematical conjectures are presented in a unified approach, and some new research material is also introduced, especially an attempt at generalizing and unifying concepts related to data set density and limiting distributions. The approach is very applied, focusing on algorithms, simulations, and big data, to help discover fascinating results. Even though some of the most exciting topics of mathematics are discussed here (including fundamental, century-old problems still unresolved as well as brand new hypotheses), most of the article can be understood by the layman. Among other things, you will learn some new ways to estimate Pi based on non-traditional experiments, or how a conjecture for prime numbers somehow generalizes to apply to Fibonacci numbers as well.