Perfect numbers

A kind of number

About Perfect numbers

A perfect number is a positive integer that equals the sum of its proper positive divisors (excluding itself). For example, 6 = 1 + 2 + 3. It is unknown whether there are infinitely many or any odd perfect numbers.

Key features

  • All known perfect numbers are even and have the form 2ᵖ⁻¹(2ᵖ − 1) where 2ᵖ − 1 is a Mersenne prime.
  • Only 51 perfect numbers are currently known.

Examples:

6, 28, 496

Further reading