A perfect number is a positive integer that is equal to the sum of its positive proper divisors.
A proper divisor is a divisor excluding the number itself
Perfect numbers were first studied by the Greeks. They knew 4 perfect numbers:
The Greeks looked at the prime factorization of the perfect numbers
and noticed the following pattern:
They discovered the Euclid–Euler theorem:
Theorem: (Euclid IX, 36)
If
is prime then is perfect
which relates perfect numbers to Mersenne primes.