Quinquadragintaseptingentillion

A quinquadragintaseptingentillion is equal to \(10^{2238}\) in the short scale and \(10^{4470}\) in the long scale by the and 's naming systemConway and Guy. (1995) "The book of Numbers" Copernicus as it is the 745th -illion number.
In the long scale, \(10^{2238}\) is called treseptuagintatrecentillion.
==Approximations==
For the short scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{2238}\) (exact) 	\(1\times10^{2238}\) (exact)
Arrow notation 	\(10\uparrow 2238\) (exact) 	\(10\uparrow 2238\) (exact)
Steinhaus-Moser Notation 	774[3] 	775[3]
Chained arrow notation 	\(10\rightarrow 2238\) (exact) 	\(10\rightarrow 2238\) (exact)
Taro's multivariable Ackermann function	A(3,7431) 	A(3,7432)
BEAF & Bird's array notation 	{10,2238} (exact) 	{10,2238} (exact)
Hyper-E notation 	E2238 (exact) 	E2238 (exact)
s(n) map 	\(s(1)^3(\lambda x.x+1)(9)\) 	\(s(1)^3(\lambda x.x+1)(10)\)
m(n) map 	m(1)(774) 	m(1)(775)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(7421)\) 	\(f_2(7422)\)
Hardy hierarchy 	\(H_{\omega^2}(7421)\) 	\(H_{\omega^2}(7422)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3 2+\omega^2 2+\omega 3+8}}(10)\) (exact)	\(g_{\omega^{\omega^3 2+\omega^2 2+\omega 3+8}}(10)\) (exact)
For the long scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{4470}\) (exact) 	\(1\times10^{4470}\) (exact)
Arrow notation 	\(10\uparrow 4470\) (exact) 	\(10\uparrow 4470\) (exact)
Steinhaus-Moser Notation 	1418[3] 	1419[3]
Chained arrow notation 	\(10\rightarrow 4470\) (exact) 	\(10\rightarrow 4470\) (exact)
Taro's multivariable Ackermann function	A(3,14846) 	A(3,14847)
BEAF & Bird's array notation 	{10,4470} (exact) 	{10,4470} (exact)
Hyper-E notation 	E4470 (exact) 	E4470 (exact)
s(n) map 	\(s(1)^3(\lambda x.x+1)(10)\) 	\(s(1)^3(\lambda x.x+1)(11)\)
m(n) map 	m(1)(1418) 	m(1)(1419)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(14835)\) 	\(f_2(14836)\)
Hardy hierarchy 	\(H_{\omega^2}(14835)\) 	\(H_{\omega^2}(14836)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3 4+\omega^2 4+\omega 7}}(10)\) (exact)	\(g_{\omega^{\omega^3 4+\omega^2 4+\omega 7}}(10)\) (exact)
== Sources ==
== See also ==
Category:Numbers
Category:Class 2
Category:Illion
Category:Numbers with 1000 to 1000000 digits
Category:Powers of 10 with squarefree exponent
Category:Tier 1 -illion numbers