So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. Meanwhile, perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. The numbers p corresponding to Mersenne primes must themselves be prime, although not all primes p lead to Mersenne primes-for example, 2 11 − 1 = 2047 = 23 × 89. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Logarithmic graph of the number of digits of the largest known prime by year, nearly all of which have been Mersenne primes
