Perfect number

In mathematics, a perfect number is a positive integer whose proper divisors sum to the number itself. For instance, 6 is a perfect number, as the proper divisors of 6 are 1, 2, and 3, and 1+2+3=6. In contrast, 4 is not a perfect number, as the proper divisors of 4 are 1 and 2, and $\scriptstyle 1+2\neq 4$. Although the name perfect suggests that these integers have some importance, they have remained little more than a curiosity since the name was coined thousands of years ago. Still, the study and search for perfect numbers has occupied and fascinated many influential mathematicians, notably Euclid, Fermat, and Euler. Also, the search for perfect numbers is still ongoing indirectly through the Great Internet Mersenne Prime Search (GIMPS), and the search for and enumeration of the properties of odd perfect numbers remains a topic of current research.