Octoseptuagintaseptingentillion

An octoseptuagintaseptingentillion is equal to \(10^{2337}\) in the short scale and \(10^{4668}\) in the long scale by the and 's naming systemConway and Guy. (1995) "The book of Numbers" Copernicus as it is the 778th -illion number.
In the long scale, \(10^{2337}\) is called novemoctogintatrecentilliard.
==Approximations==
For the short scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{2337}\) (exact) 	\(1\times10^{2337}\) (exact)
Arrow notation 	\(10\uparrow 2337\) (exact) 	\(10\uparrow 2337\) (exact)
Steinhaus-Moser Notation 	804[3] 	805[3]
Chained arrow notation 	\(10\rightarrow 2337\) (exact) 	\(10\rightarrow 2337\) (exact)
Taro's multivariable Ackermann function	A(3,7760) 	A(3,7761)
BEAF & Bird's array notation 	{10,2337} (exact) 	{10,2337} (exact)
Hyper-E notation 	E2337 (exact) 	E2337 (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)(804) 	m(1)(805)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(7750)\) 	\(f_2(7751)\)
Hardy hierarchy 	\(H_{\omega^2}(7750)\) 	\(H_{\omega^2}(7751)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3 2+\omega^2 3+\omega 3+7}}(10)\) (exact)	\(g_{\omega^{\omega^3 2+\omega^2 3+\omega 3+7}}(10)\) (exact)
For the long scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{4668}\) (exact) 	\(1\times10^{4668}\) (exact)
Arrow notation 	\(10\uparrow 4668\) (exact) 	\(10\uparrow 4668\) (exact)
Steinhaus-Moser Notation 	1473[3] 	1474[3]
Chained arrow notation 	\(10\rightarrow 4668\) (exact) 	\(10\rightarrow 4668\) (exact)
Taro's multivariable Ackermann function	A(3,15503) 	A(3,15504)
BEAF & Bird's array notation 	{10,4668} (exact) 	{10,4668} (exact)
Hyper-E notation 	E4668 (exact) 	E4668 (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)(1473) 	m(1)(1474)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(15492)\) 	\(f_2(15493)\)
Hardy hierarchy 	\(H_{\omega^2}(15492)\) 	\(H_{\omega^2}(15493)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3 4+\omega^2 6+\omega 6+8}}(10)\) (exact)	\(g_{\omega^{\omega^3 4+\omega^2 6+\omega 6+8}}(10)\) (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