Quadragintaquingentillion

A quadragintaquingentillion is equal to \(10^{1623}\) in the short scale and \(10^{3240}\) in the long scale by the and 's naming systemConway and Guy. (1995) "The book of Numbers" Copernicus as it is the 540th -illion number.
In the long scale, \(10^{1623}\) is called septuagintaducentilliard.
==Approximations==
For the short scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{1623}\) (exact) 	\(1\times10^{1623}\) (exact)
Arrow notation 	\(10\uparrow 1623\) (exact) 	\(10\uparrow 1623\) (exact)
Steinhaus-Moser Notation 	586[3] 	587[3]
Chained arrow notation 	\(10\rightarrow 1623\) (exact) 	\(10\rightarrow 1623\) (exact)
Taro's multivariable Ackermann function	A(3,5388) 	A(3,5389)
BEAF & Bird's array notation 	{10,1623} (exact) 	{10,1623} (exact)
Hyper-E notation 	E1623 (exact) 	E1623 (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)(586) 	m(1)(587)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(5379)\) 	\(f_2(5380)\)
Hardy hierarchy 	\(H_{\omega^2}(5379)\) 	\(H_{\omega^2}(5380)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3+\omega^2 6+\omega 2+3}}(10)\) (exact)	\(g_{\omega^{\omega^3+\omega^2 6+\omega 2+3}}(10)\) (exact)
For the long scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{3240}\) (exact) 	\(1\times10^{3240}\) (exact)
Arrow notation 	\(10\uparrow 3240\) (exact) 	\(10\uparrow 3240\) (exact)
Steinhaus-Moser Notation 	1069[3] 	1070[3]
Chained arrow notation 	\(10\rightarrow 3240\) (exact) 	\(10\rightarrow 3240\) (exact)
Taro's multivariable Ackermann function	A(3,10760) 	A(3,10761)
BEAF & Bird's array notation 	{10,3240} (exact) 	{10,3240} (exact)
Hyper-E notation 	E3240 (exact) 	E3240 (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)(1069) 	m(1)(1070)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(10749)\) 	\(f_2(10750)\)
Hardy hierarchy 	\(H_{\omega^2}(10749)\) 	\(H_{\omega^2}(10750)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3 3+\omega^2 2+\omega 4}}(10)\) (exact)	\(g_{\omega^{\omega^3 3+\omega^2 2+\omega 4}}(10)\) (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