User blog comment:Swooped me in one hit/bnjvkldskjfvgdkl/@comment-29310326-20170214223525/@comment-30754445-20170214232916

Assuming this number is supposed to represent a new start (I don't see any arrows or g's in there, which is a good thing) - it's not bad.

Before I give more feedback, one minor quibble: You've gone from 2 factorials to 5 to 8. It isn't clear whether you wanted the number of factorials to just double at every step (2,4,8,16), or to double and then add 1 (2,5,11,23). Either way, you made a typo there. Any way, from here now, I'll assume you meant simple doubling without adding one.

The good:

The definition is tight and simple

For a 100% original construction, it is respectably big. Much bigger than a googolplex (but still nowhere close to Graham or even g1, but that's to be expected for a first attempt)

The bad:

Only one complaint really: All the random numbers in there are unnecessary. What's the point of writing " 2^10^20^40^80^7687" when you can simply write "10^10^10^10^10^10"? Or - since your entire number is based on factorials - you could use factorials there as well: "the number of doublings is 6!!!!!!!" would do.



So, just how big is this number?

Well, since the number of factorials doubles at each step, the final number of factorials is:

2^[number of steps] = 2^2^10^20^40^80^7687 ~ 10^10^10^10^10^10^10 = 10↑↑7

And repeated factorials are as strong as power-towers, so your number is about:

Your Number ~ 10↑↑10↑↑7 ~ G2.85 (in my notation)

And that's... big. Not only is this number larger than a googolplex, it is larger than what most people could come up with if you asked them to "define the biggest number you can think of" (Graham's number doesn't count, because even though many people have heard of it in passing, the vast majority of them have no idea how it is constructed)

So that's a good first attempt.

Oh, and just to wet your appetite a bit: g1 is something like H2.4. Your only one letter away from getting there :-)

Now, I'm sure you have some questions about what I've just written, so - fire away.