List of perfect numbers

The following is a list of the known perfect numbers, and the exponents p that can be used to generate them (using the expression 2p−1× (2p − 1)) whenever 2p − 1 is a Mersenne prime. All even perfect numbers are of this form. It is not known whether there are any odd perfect numbers. As of 2019 there are 51 known perfect numbers in total. For even perfect numbers, the ratio p / digits approaches log(10) / log(4) = 1.6609640474...

List of perfect numbers

The following is a list of the known perfect numbers, and the exponents p that can be used to generate them (using the expression 2p−1× (2p − 1)) whenever 2p − 1 is a Mersenne prime. All even perfect numbers are of this form. It is not known whether there are any odd perfect numbers. As of 2019 there are 51 known perfect numbers in total. For even perfect numbers, the ratio p / digits approaches log(10) / log(4) = 1.6609640474...