A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. For example, the number 6 is a perfect number because its divisors are 1, 2, and 3, and when you add them together (1 + 2 + 3), the sum is 6. The concept of perfect numbers has been studied since ancient times, with the first known perfect number being 6. Another example is 28, which has divisors 1, 2, 4, 7, and 14, and their sum also equals 28. Perfect numbers are closely related to Mersenne primes, which help in their identification.