Perfect Numbers

I was just doing some work and listening to one of my favorite songs, "Tonight You're Perfect" by the band New Politics.  As I was listening to the song, I was reminded of something we learned in class last week - perfect numbers!

Recall that perfect numbers are numbers whose sum of their proper factors is equal to the number itself.

For example, 6 is a perfect number because its proper factors are 1, 2, and 3.  The sum of 1+2+3 is 6.

By 1999, only 38 perfect numbers have been found!

Can you determine the next three perfect numbers after 6?

Is it possible for a perfect number to be a prime number?

Are all perfect numbers even?

Is it possible to have a perfect number that is prime?

Share your answers as a comment!