Super-leviathan

Super-leviathan is \(9^{9^{9}}\), which is the largest number that can be written using only three digits.Clifford Pickover. Keys to Infinity Wiley. 1995. ISBN 978-0471118572 p.102 By using tetration, it can be written as 39 (read as "to-the-third-nine"). It is equal to \(9^{387,420,489} \approx 4.281247731757470 \times 10^{369,693,099}\). It has 369,693,100 digits.
Cookiefonster calls this number Ulysses Number.Cookiefonster. Pointless Gigantic List of Numbers - Part 2 (1,000,000 ~ 10^10^1,000,000)
Full decimal expansion is calculated.Hans Havermann. 9^9^9 in 33 volumes 2004-01-06.Fish. Full decimal expansion of super-leviathan 2024-09-23.OEIS. A241298 Decimal expansion of 9^(9^9) = 9^^3.
==Approximations==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(4.281\times10^{369\,693\,099}\)	\(4.282\times10^{369\,693\,099}\)
Arrow notation 	\(9\uparrow\uparrow3\) 	\(9\uparrow\uparrow3\)
Steinhaus-Moser Notation 	8[3][3] 	9[3][3]
Copy notation 	3[3[9]] 	4[4[9]]
Taro's multivariable Ackermann function	A(3,A(3,27)) 	A(3,A(3,28))
Pound-Star Notation 	#*((1))*6798 	#*((1))*6799
BEAF 	{9,3,2} 	{9,3,2}
Hyper-E notation 	E[9]1#3 	E[9]1#3
Bashicu matrix system 	(0)(1)[5] 	(0)(1)[6]
Hyperfactorial array notation 	(11!)! 	(12!)!
Fast-growing hierarchy 	\(f_2(f_2(25))\) 	\(f_2(f_2(26))\)
Hardy hierarchy 	\(H_{\omega^22}(25)\) 	\(H_{\omega^22}(26)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^\omega}}(9)\)	\(g_{\omega^{\omega^\omega}}(9)\)
== Sources ==
== See also ==
* 65,536
* 7,625,597,484,987
* 34
* 35
* 36
* 37
* 38
* 310
* 52
Category:Numbers
Category:Class 3
Category:Powers of 3
Category:Tetration
Category:Lower class 3
Category:Numbers with peer-reviewed source