Tresviginticentillion

A tresviginticentillion is equal to \(10^{372}\) in the short scale and \(10^{738}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4] as it is the 123rd -illion number.

In the long scale, \(10^{372}\) is called duosexagintillion.

Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{372}\) (exact)
Arrow notation	\(10\uparrow 372\) (exact)
Steinhaus-Moser Notation	167[3]	168[3]
Chained arrow notation	\(10\rightarrow 372\) (exact)
Taro's multivariable Ackermann function	A(3,1232)	A(3,1233)
BEAF & Bird's array notation	{10,372} (exact)
Hyper-E notation	E372 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(7)\)	\(s(1)^3(\lambda x.x+1)(8)\)
m(n) map	m(1)(167)	m(1)(168)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)[28]	(0)(0)(0)(0)(0)(0)(0)(0)[29]
Fast-growing hierarchy	\(f_2(1225)\)	\(f_2(1226)\)
Hardy hierarchy	\(H_{\omega^2}(1225)\)	\(H_{\omega^2}(1226)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 3+\omega 7+2}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{738}\) (exact)
Arrow notation	\(10\uparrow 738\) (exact)
Steinhaus-Moser Notation	298[3]	299[3]
Chained arrow notation	\(10\rightarrow 738\) (exact)
Taro's multivariable Ackermann function	A(3,2448)	A(3,2449)
BEAF & Bird's array notation	{10,738} (exact)
Hyper-E notation	E738 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(8)\)	\(s(1)^3(\lambda x.x+1)(9)\)
m(n) map	m(1)(298)	m(1)(299)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)(0)[27]	(0)(0)(0)(0)(0)(0)(0)(0)(0)[28]
Fast-growing hierarchy	\(f_2(2440)\)	\(f_2(2441)\)
Hardy hierarchy	\(H_{\omega^2}(2440)\)	\(H_{\omega^2}(2441)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 7+\omega 3+8}}(10)\) (exact)

Main article: -illion