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The tethrathoth-ex-grand tethrathoth-ex-grand tethrathoth is equal to E100#^^#100#(1+E100#^^#100#(1+E100#^^#100)) in Extended Cascading-E Notation.[1] The term was coined by Sbiis Saibian.

## Etymology

The name of this number is based on the number tethrathoth-ex-grand tethrathoth and the number "grand tethrathoth".

## Approximations

Notation Approximation
BEAF $$\{100,\text{tethrathoth-ex-grand tethrathoth}+2,2(X\uparrow\uparrow X)2\}$$[2]
Bird's array notation $$\{100,\text{tethrathoth-ex-grand tethrathoth}+2,2[1\backslash2]2\}$$
Hyperfactorial array notation $$\text{tethrathoth-ex-grand tethrathoth}![2,1,1,1,2]$$
Fast-growing hierarchy $$f_{\varepsilon_0+1}(\text{tethrathoth-ex-grand tethrathoth}+1)$$
Hardy hierarchy $$H_{\varepsilon_0\omega}(\text{tethrathoth-ex-grand tethrathoth}+1)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega2})}(\text{tethrathoth-ex-grand tethrathoth}+1)$$

## Sources

1. Saibian, Sbiis. 4.3.7 Extended Cascading-E Numbers Part IOne to Infinity. Retrieved 2015-12-30.
2. Using particular notation $$\{a,b (A) 2\} = A \&\ a$$ with prime b.