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The tethraterthoth is equal to E100#^^#100#^^#100#^^#100 = E100#^^#*#4 in Extended Cascading-E Notation.[1][2] The term was coined by Sbiis Saibian.

## Etymology

The name of this number is based on Greek prefix "tetra-" and the number "tethrathoth".

## Approximations in other notations

Notation Approximation
BEAF $$\{100,100 (X \uparrow\uparrow X) 4\}$$[3]
Bird's array notation $$\{100,100 [1 \backslash 2] 4\}$$
Hyperfactorial array notation $$100![1,3,1,1,2]$$
X-Sequence Hyper-Exponential Notation $$100\{(X\uparrow\uparrow X)*3\}100$$
Fast-growing hierarchy $$f_{\varepsilon_0 3}(100)$$
Hardy hierarchy $$H_{\varepsilon_0^3}(101)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega2}2+\varepsilon_{\Omega+1})}(100)$$

## Sources

1. 4.3.5 Cascading-E Numbers by Sbiis Saibian
2. Sbiis Saibian's Ultimate Large Numbers List - Part III
3. Using particular notation $$\{a,b (X \uparrow\uparrow X) c \#\}$$ for $$\{X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) c-1 \#\}$$