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The grand hecato-tethrathoth (also called grand tethrafact[1]) is equal to E100(#^^#)^#100#2 in Extended Cascading-E Notation.[2] The term was coined by Sbiis Saibian.

Etymology

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

Approximations in other notations

Notation Approximation
BEAF $$\{100,\text{hecato-tethrathoth} (X \uparrow\uparrow X*X) 2\}$$[3]
Bird's array notation $$\{100,\text{hecato-tethrathoth} [2 \backslash 2] 2\}$$
Hyperfactorial array notation $$(100![1,1,[1],1,2])![1,1,[1],1,2]$$
X-Sequence Hyper-Exponential Notation $$100\{(X\uparrow\uparrow X)^{X}\}100\{(X\uparrow\uparrow X)^{X}\}100$$
Fast-growing hierarchy $$f_{\varepsilon_0^\omega}(f_{\varepsilon_0^\omega}(100))$$
Hardy hierarchy $$H_{\varepsilon_0^{\varepsilon_0^\omega} 2}(99)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega2}^{\vartheta(\varepsilon_{\Omega2}^\omega)})}(100)$$

Sources

1. Saibian, Sbiis. 4.3.7 Extended Cascading-E Numbers Part IOne to Infinity. Retrieved 2017-04-09.
2. Sbiis Saibian's Ultimate Large Numbers List - Part III
3. Using particular notation $$\{a,b (A) 2\} = A\ \&\ a$$ with prime b.