Octoquinquagintaquingentillion

An octoquinquagintaquingentillion is equal to \(10^{1677}\) in the short scale and \(10^{3348}\) in the long scale by the and 's naming systemConway and Guy. (1995) "The book of Numbers" Copernicus as it is the 558th -illion number.
In the long scale, \(10^{1677}\) is called novenseptuagintaducentilliard.
==Approximations==
For the short scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{1677}\) (exact) 	\(1\times10^{1677}\) (exact)
Arrow notation 	\(10\uparrow 1677\) (exact) 	\(10\uparrow 1677\) (exact)
Steinhaus-Moser Notation 	603[3] 	604[3]
Chained arrow notation 	\(10\rightarrow 1677\) (exact) 	\(10\rightarrow 1677\) (exact)
Taro's multivariable Ackermann function	A(3,5567) 	A(3,5568)
BEAF & Bird's array notation 	{10,1677} (exact) 	{10,1677} (exact)
Hyper-E notation 	E1677 (exact) 	E1677 (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)(603) 	m(1)(604)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(5558)\) 	\(f_2(5559)\)
Hardy hierarchy 	\(H_{\omega^2}(5558)\) 	\(H_{\omega^2}(5559)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3+\omega^2 6+\omega 7+7}}(10)\) (exact)	\(g_{\omega^{\omega^3+\omega^2 6+\omega 7+7}}(10)\) (exact)
For the long scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{3348}\) (exact) 	\(1\times10^{3348}\) (exact)
Arrow notation 	\(10\uparrow 3348\) (exact) 	\(10\uparrow 3348\) (exact)
Steinhaus-Moser Notation 	1100[3] 	1101[3]
Chained arrow notation 	\(10\rightarrow 3348\) (exact) 	\(10\rightarrow 3348\) (exact)
Taro's multivariable Ackermann function	A(3,11118) 	A(3,11119)
BEAF & Bird's array notation 	{10,3348} (exact) 	{10,3348} (exact)
Hyper-E notation 	E3348 (exact) 	E3348 (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)(1100) 	m(1)(1101)
Bashicu matrix system 	(0)(1)[3] 	(0)(1)[4]
Fast-growing hierarchy 	\(f_2(11108)\) 	\(f_2(11109)\)
Hardy hierarchy 	\(H_{\omega^2}(11108)\) 	\(H_{\omega^2}(11109)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3 3+\omega^2 3+\omega 4+8}}(10)\) (exact)	\(g_{\omega^{\omega^3 3+\omega^2 3+\omega 4+8}}(10)\) (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