even perfect number

[jas_fluidm]

Over 2300 years ago Euclid proved that If 2^(k)-1 is a prime number (it would be a Mersenne prime), then 2^(k-1)(2^(k)-1) is a perfect number. A few hundred years ago Euler proved the converse (that every even perfect number has this form).  It is still unknown if there are any odd perfect numbers (but if there are, they are large and have many prime factors).

[Masuma Parvin]

All even perfect numbers are a power of two times a Mersenne prime.

[tasnuva]

Nice post.