Centretillion

Not to be confused with trecentillion.

The centretillion^[1], trecentillion^[2] or trescentillion^[3] is equal to \(10^{312}\) in short scale. It is equal to \(10^{618}\) in long scale. It is 313 digits long in short scale, or 619 digits long in long scale.

Approximations

For short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{312}\)
Arrow notation	\(10\uparrow312\)
Steinhaus-Moser Notation	144[3]	145[3]
Copy notation	9[312]	1[313]
Chained arrow notation	\(10→312\)
H* function	H(103)
Taro's multivariable Ackermann function	A(3,1033)	A(3,1034)
Pound-Star Notation	#((844))11	#((845))11
BEAF	{10,312}
Hyper-E notation	E312
Bashicu matrix system	(0)(0)(0)(0)(0)(0)[74989]	(0)(0)(0)(0)(0)(0)[74990]
Bird's array notation	{10,312}
Hyperfactorial array notation	172!	173!
Strong array notation	s(10,312)
Fast-growing hierarchy	\(f_2(1026)\)	\(f_2(1027)\)
Hardy hierarchy	\(H_{\omega^2}(1026)\)	\(H_{\omega^2}(1027)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^23+\omega+2}}(10)\)

For long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{618}\)
Arrow notation	\(10\uparrow618\)
Steinhaus-Moser Notation	256[3]	257[3]
Copy notation	9[618]	1[619]
Chained arrow notation	\(10\rightarrow618\)
H* function	H(205)
Taro's multivariable Ackermann function	A(3,2049)	A(3,2050)
Pound-Star Notation	#((485))15	#((486))15
BEAF	{10,618}
Hyper-E notation	E618
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)[67317]	(0)(0)(0)(0)(0)(0)(0)[67318]
Hyperfactorial array notation	301!	302!
Fast-growing hierarchy	\(f_2(2041)\)	\(f_2(2042)\)
Hardy hierarchy	\(H_{\omega^2}(2041)\)	\(H_{\omega^2}(2042)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^26+\omega+8}}(10)\)

Sources

[1] Illion Numbers

[2] ttps://web.archive.org/web/20201109042552/http://users.skynet.be/nizgorur/very_big_numbers.htm

[3] ttps://sites.google.com/site/largenumbers/home/2-4/AAA

[1]

[2]

[3]

Centretillion

Approximations

Sources

See also

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