A Study on Odd Perfect Numbers

A perfect number is defined as a number n for which the sum of the divisors of n equals 2n. All perfect numbers currently known are even. In this project, the idea of an odd perfect number was investigated through a computer program. This project explores some of the theory behind an odd perfect number in order to be able to optimize a computer program to search for one efficiently. Because it has been proven that no odd perfect number exists below 101500, the program must start at a number slightly above that to effectively search for one. This is where the theory behind odd perfect numbers is used, as it is impossibly slow to search every odd number above 101500 until an odd perfect is found. At the end of the optimization process, the program was 2 103778times faster than the original program. In the course of this work, the program searched two trillion numbers above 101500for potential odd perfect numbers without finding one