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Not to be confused with tethrathruli-godgathor.

The tethrathruli-godhathor (formerly tethrathruli-godextatothol) is equal to 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 tethraduli-godextathol and the Latin prefix "trio-", meaning 3.

## Approximations in other notations

Notation Approximation
BEAF $$\{100,100((X \uparrow\uparrow X)^3*X^{X^{X^{X^{X^X}}}}) 2\}$$[2]
Bird's array notation $$\{100,100 [1[1[1,2]2]2[1\backslash 2]3\backslash 2] 2\}$$
Hyperfactorial array notation $$100![1,[1,[1,[1,[1,1,2,2],1,3],1,4],3,1,2],[1],1,2]$$
Fast-growing hierarchy $$f_{\varepsilon_0^{\varepsilon_0^2\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}}(100)$$
Hardy hierarchy

$$H_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^2\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}}}(100)$$

Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega 2}^{\varepsilon_{\Omega 2}^2\Omega^{\Omega^{\Omega^{\Omega^{\Omega^\omega}}}}})}(100)$$

## Sources

1. Saibian, Sbiis. 4.3.7 Extended Cascading-E Numbers Part IOne to Infinity. Retrieved 2015-12-18.
2. Using particular notation $$\{a,b (A) 2\} = A \&\ a$$ with prime b.