Two Equations for Perfect Numbers

Abstract

Perfect numbers have not been documented as numerically even. This document shows that the current perfect numbers can be compiled from the difference between two binary numbers. There are two equations that compile these perfect numbers. As noted by previous mathematicians, perfect numbers that are currently known end in either 6 or 28. To compile perfect numbers that end in the numerical number 6 (except for the perfect number, 6, itself), the difference between two binary numbers is represented by 2*(256^m) - (16^m). To compile perfect numbers that end in the numerical number 28 (except for the perfect number, 28, itself), the difference between two binary numbers is represented by 2*(64^n) - (8^n). The numerical values of m and n do not have a definite equation that determines their values. However, there are equations that can eliminate possibilities such as X= 4m +1 and Y= 3n +1, with X and Y being prime. These equations are explained more in detail later on in this document.