Leviathan number

The Leviathan number is equal to \(10^{666}! \approx 10^{6.6556570552\times10^{668}}\), where \(n!\) denotes the factorial.Clifford Pickover. Keys to Infinity Wiley. 1995. ISBN 978-0471118572 p.98Leviathan Number from Wolfram MathWorldNotable Properties of Specific Numbers (page 22) at MROB 
The number was defined by scientific author Clifford Alan Pickover in 1995. It has been shown to have \(2.5\times10^{665} - 143\) trailing zeros.
==Approximations==
Notation 	Lower bound 	Upper bound
Arrow notation 	\(284\uparrow312\uparrow268\) 	\(926\uparrow106\uparrow330\)
Down-arrow notation 	\(418\downarrow\downarrow256\) 	\(299\downarrow\downarrow271\)
Steinhaus-Moser Notation 	273[3][3] 	274[3][3]
Copy notation 	5[5[669]] 	6[6[669]]
H* function 	H(221H(221)) 	H(222H(221))
Taro's multivariable Ackermann function	A(3,A(3,2220)) 	A(3,A(3,2221))
Pound-Star Notation 	#*((1))*((8))*12 	#*((1))*((9))*12
BEAF 	{284,{312,268}} 	{926,{106,330}}
Hyper-E notation 	E[418]255#2 	E[299]270#2
Bashicu matrix system 	(0)(1)[47] 	(0)(1)[48]
Hyperfactorial array notation 	(320!)! 	(321!)!
Fast-growing hierarchy 	\(f_2(f_2(2212))\) 	\(f_2(f_2(2213))\)
Hardy hierarchy 	\(H_{\omega^{22}}(2212)\) 	\(H_{\omega^{22}}(2213)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^{\omega^{26}+\omega6+86}}}(10)\)	\(g_{\omega^{\omega^{\omega^{26}+\omega6+87}}}(10)\)
== See also ==
*Beast number
*Super-leviathan
*Legion's number of the first and second kind
== Sources ==
ja:レヴィアタン数
Category:Numbers
Category:Class 3
Category:Orders of symmetric groups
Category:Upper class 3
Category:Numbers with peer-reviewed source