Minecraftplex

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Minecraftplex (Not to be confused with Mineplex, a popular Minecraft server) is a large number named by Austin Hourigan in a video called "Minecraft DECODED! How Many Diamonds Exist? | The SCIENCE... of Minecraft". It is equal to 10¹⁰²¹⁵, or a 1 followed by 100 septuagintillion zeroes. It is 10²¹⁵+1 digits long.

Writing down the full decimal expansion would take 100 octosexagintillion (10²⁰⁹) books of 400 pages each, with 2,500 digits on each page (except for the first, which would have 2,501). It is slightly bigger than a septuagintillionplex (10¹⁰²¹³).

History

Minecraft DECODED! How Many Diamonds Exist? The SCIENCE... of Minecraft

Hourigan invented this number while attempting to one-up MatPat's Marioplex (the number of possible, completable, and fun levels in the game Super Mario Maker) by calculating the number of different placements of blocks in every Minecraft world possible. The number first appears at the 15:08 timestamp.

Size

The only direct reference Hourigan gives to the size of the number is that it "can't actually be displayed on anything since it outnumbers the atoms in the universe by a fair amount". It is roughly equal to equations like ((10^10^100)^(10^100))^(10^15), a (googolplex^googol)^quadrillion, or even (marioplex^2,500,000,000)^(12431^15). The entire number in The English name of a number, is insanely long, just look.

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Approximations

Notation	Lower bound	Upper bound
Arrow notation	\(10\uparrow10\uparrow215\)
Down-arrow notation	\(10\downarrow\downarrow216\)
Chained arrow notation	\(10\rightarrow(10\rightarrow215)\)
Steinhaus-Moser Notation	105[3][3]	106[3][3]
Copy notation	9[9[215]]	1[10[108]]
H* function	H(33H(70))	H(34H(70))
Taro's multivariable Ackermann function	A(3,A(3,712))	A(3,A(3,713))
Pound-Star Notation	#*((1))*((160))*7	#*((1))*((161))*7
BEAF	{10,{10,215}}
Hyper-E notation	E215#2
Bashicu matrix system	(0)(1)[26]	(0)(1)[27]
Hyperfactorial array notation	(126!)!	(127!)!
Fast-growing hierarchy	\(f_2(f_2(706))\)	\(f_2(f_2(707))\)
Hardy hierarchy	\(H_{\omega^22}(706)\)	\(H_{\omega^22}(707)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^{\omega^22+\omega+5}}}(10)\)

Gallery

How the Minecraftplex was calculated

The minecraftplex without nested exponents