Number Choosing Contest.

Let H_n(a,b) be defined as such:



And:

Let S(a,b) =
H_n(a,b) where
n = Ackermann(S(a-1,b),S(a,b-1)))

I guess the following:

S(Graham's Number, Twelve Googol)

S(Largest Known Prime, Second Largest Known Prime)

S(The second number I guessed, The first number I guessed)

S(The number of board states in Chess regardless of legality or supply of pieces, The number of possible Go games)

292292292292

*insert any of those first four "numbers" here*: breaks XYZ & well, um:
1: all of these DEFINITELY BREAK RULE 1
2: *shrug*
3: it is 99.999999999999999999999999999999999999999999999999999...% certain that all of these break rule 3.
4: fuck no I'm not even going to try
5: double fuck no

292292292292: breaks YZ & 1 and 3. Somehow, this is the first number to pass rule 5.

Edit: sorry

It's okay. That was absolutely my fault.

wait why is it 1630767959559389054594297182400609699502827817

it's just "i love you bby ;))))" written in binary

It is also the binary representation of 1630767959559389054594297182400609699502827817. Since "i love you bby ;))))" is not a number, I was not able to evaluate it, though I suppose I could give it a try:

i love you bby ;)))): breaks WXYZ & 1, 2, *distressed whine* 3, 4 and 5.