My Version of Sam's Number

Even though DeepLineMadom pointed out that Sam's number is not considered to be a defined number at all, I still want to explain my version of Sam's number just for a 'joke' for you guys.

Note that m and n are positive integers.

1. M(n) = The smallest positive integer bigger than any finite integer named by n mathematicians in n centuries.

2. M^m(n) = M(M(M ... (M(n)) ... )) (m iterations of the M function)

3. M_{α + 1}(n) = M_{α}^n(n) (similar to the fast-growing hierarchy) where α is either an positive integer or a transfinite ordinal.

4. M_{0}(n) = M(n)

5. M_{α}(n) = M_{α[n]}(n) if α is a limit ordinal.

M(0) = 0

M(1) >>>>> Rayo's number???

M(2) = ??????????

Sam's number = 

M_{ω^{CK}_{ψ0(ε_{Ω_{Ω_{Ω_{Ω_{Ω_{ω_1^{CK}}}}}} * Φ_1(1) + 1}) * f_{ψ(K(2;0) * M(2;0) * I(1, 0, 0, 0) * Ω(1, 0, 0)) * E100*(*(*(*(*(*(#)))))){&(&(&(#))),#+1,1,2}^^^^^#^^^^^#>#^^^^^#>#^^^^^#>#^^^^^#>#^^^^^#>#^^^^^(#+#+#+#+#)^^^^^#####*#*#*#*#*#**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^###########{#{#{#{#{#{#{#{#{#{#^^^^^#^^^^#^^^#^^#^#*##+#}#}#}#}#}#}#}#}#}#}###########*##########100##########100#########100########100#######100######100#####100####100###100##100#100##1#2}(FOOT^{10}(10^100) + Rayo(10^100)) + {10, 100 / 2}}(Ultimate oblivion + large number garden number), which is an uncomputable salad number.

There are at least 10! = 3,628,800 arrangements for the capitalizations for the number Sam's number.

(Referred to the notation in this video [modified])