A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. In other words, a perfect number is a number that is half the sum of all of its positive divisors including itself. For example, 6 is a perfect number because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. The first few perfect numbers are 6, 28, 496, and 8128. All perfect numbers are even numbers. Euclid, over two thousand years ago, showed that all even perfect numbers can be represented by N = 2p-1(2p -1) where p is a prime for which 2p -1 is a Mersenne prime. The search for perfect numbers is ongoing, and as of December 2018, 51 Mersenne primes are known, and therefore 51 even perfect numbers. It is still unknown whether odd perfect numbers exist or not.