quality:correction
Perfect numbers

Mersenne primes M are closely connected to perfect numbers. In the 4th century BC, Euclid proved that if 2 − 1 is prime, then 2 (2 − 1) is a perfect number. In the 18th century, Leonhard Euler proved that, conversely, all even perfect numbers have this form. This is known as the Euclid–Euler theorem. It is unknown whether there are any odd perfect numbers.

An alternative form of Perfect Numbers (not affecting the essence): If (M = 2 n − 1) {\displaystyle (M=2^{n}-1)} is a prime number, then P = M (M + 1) / 2 {\displaystyle P=M(M+1)/2} is a Perfect Number. (Perfect Numbers are Triangular Numbers whose base is a Mersenne Prime.)