good number hierarchy

2000
is beaten by
2048 = 2^11
is beaten by
2^256 = 2^(2^8) = 2^(2^(2^3))
is beaten by
2^16 = 2^(2^4) = 2^(2^(2^2)) = 2^(2^(2^(2^1))) = 2^(2^(2^(2^(2^0))))

= 2 tetrated to the 4 = 2 tet (2 tet 2)

= 2 pentated to the 3

is beaten by

4

= 2 [anything] 2

yes, I am in agreement.

the three hiding in 256 always bothered me, it was such a perfect number otherwise.

8658 is the best number.

6+28+496+8128 = 8658 (first four perfect numbers)
666*13 = 8658

no.

first of all, that's only got a single 2 in there. it's just barely even.

second, what's so special about the first four perfect numbers? why not the first five? or first 100? it's completely arbitrary.

third, 666 is of no mathematical importance, and 13 is of very little. both are horribly ugly, 666 having far too many threes (and sixes, which I personally consider worse), 13 having no factors at all.

So I'm guessing 7625597484987 is right out?

If it takes 2 to tango, how many tangos are in 4? 256?

So I'm guessing 7625597484987 is right out?

Well, it's better than say 7625597484988. But still nowhere near as good as anything 2^2^n.