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Octalogue
100000.....00000    7

100000.....00000

100000.....00000
100000.....00000
10000000000
Octalogue in zeroes
The octalogue is equal to E1#8 = EEEEEEEE1 = 10^10^10^10^10^10^10^10 = 10^^8, using Hyper-E notation and up-arrow notation, respectively.[1][2] The term was coined by Sbiis Saibian.

Andre Joyce has given an alternate name megistron,[3] which is confusingly also an incorrect spelling of megiston.

Etymology Edit

The name of this number is based on Greek prefix "octa-" and the word "logarithm".

Approximations in other notations Edit

Notation Approximation
Scientific notation $$10^{10^{10^{10^{10^{10^{10^{10}}}}}}}$$ (exact value)
Up-arrow notation $$10 \uparrow\uparrow 8$$ (exact value)
Chained arrow notation $$10 \rightarrow 8 \rightarrow 2$$ (exact value)
BEAF $$\{10,8,2\}$$ (exact value)
Hyperfactorial Array Notation $$(((((((13!0)!0)!0)!0)!0)!0)!0$$
Fast-growing hierarchy $$f_2(f_2(f_2(f_2(f_2(f_2(f_2(28))))))))$$
Hardy hierarchy $$H_{(\omega^2) 7}(28)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}}}(10)$$ (exact value)

Sources Edit

1. Saibian, Sbiis. Hyper-E Numbers
2. Sbiis Saibian's Ultimate Large Numbers List
3. [1]