> By perfect numbers, do you mean numbers for which their factors add up to their total? E.g., 6=1*2*3, 1+2+3=6. I think I remember one Euclidian proof in the elements that there had to be a infinite number of those.... having something to do with using a lower perfect number to always get the next one.
>

I don't remember seeing that, but it doesn't really make sense to use one perfect number to get the next one, because you can't do that.

> Incidentally, I believe the largest prime number currently known is 2^(13,466,917)-1. That's about 4 million digits.

Yes it is. That's what we're planning to use. When we make it perfect, it'll be almost exactly twice as long, making it 8.2 million digits.