The gulgolplex is equal to E(E100#100#100#100#100#100) using Hyper-E notation.[1] It is equal to 1 followed by gulgol zeroes or 10gulgol. The term was coined by Sbiis Saibian to show how negligible the effect the -plex prefix gives to octational level numbers. It is gulgol+1 digits long.

Etymology

The 2 parts of the name, "gulgol" and "-plex" means E100#100#100#100#100#100 and 10n which basically means 1 followed by n zeroes, which formed 10(E100#100#100#100#100#100) (1 followed by gulgol zeroes) when concentrated from left to right. So the full name indicates how the number is constructed.

Approximations in other notations

Notation Approximation
Up-arrow notation \(10^{100 \uparrow^{6} 101}\)
Chained arrow notation \(10→(100 \rightarrow 101 \rightarrow 6)\)
BEAF \(\{10,\{100,101,6\}\}\)
Hyperfactorial array notation \(\text{gulgol}!\)
Fast-growing hierarchy \(f_2(f_7(100))\)
Hardy hierarchy \(H_{\omega^2+\omega^7}(100)\)
Slow-growing hierarchy \(g_{\omega^{\varphi(5,0) + 1}}(100)\)

Sources

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