Quattuorcentillion

A quattuorcentillion is equal to \(10^{315}\) in the short scale and \(10^{624}\) in the long scale by Conway and Guy's naming systemConway and Guy. (1995) "The book of Numbers" Copernicus as it is the 104th -illion number.
The least example \(n\) of \(\pi(n) > \mathrm{li}(n)\) must be smaller than 14 quattuorcentillion.Y. Saouter and P. Demichel (2010) A sharp region where π(x) - li(n) is positive. Math. Comp. 79, 2395-2405. Theorem 6.3
In the long scale, \(10^{315}\) is called duoquinquagintilliard.
==Approximations==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{315}\) 	\(1\times10^{315}\)
Arrow notation 	\(10\uparrow315\) 	\(10\uparrow315\)
Steinhaus-Moser Notation 	145[3] 	146[3]
Copy notation 	9[315] 	10[158]
Chained arrow notation 	10→315 	10→315
H* function 	H(104) 	H(104)
Taro's multivariable Ackermann function	A(3,1043) 	A(3,1044)
Pound-Star Notation 	#*((1173))*11 	#*((1174))*11
BEAF & Bird's array notation 	{10,315} 	{10,315}
Hyper-E notation 	E315 	E315
Bashicu matrix system 	(0)(0)(0)(0)(0)(0)[83536] 	(0)(0)(0)(0)(0)(0)[83537]
Hyperfactorial array notation 	173! 	174!
Fast-growing hierarchy 	\(f_2(1\,036)\) 	\(f_2(1\,037)\)
Hardy hierarchy 	\(H_{\omega^2}(1\,036)\) 	\(H_{\omega^2}(1\,037)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^23+\omega+5}}(10)\)	\(g_{\omega^{\omega^23+\omega+5}}(10)\)
== Sources ==
== See also ==
Category:Numbers
Category:Class 2
Category:Illion
Category:Numbers with 101 to 999 digits
Category:Tier 1 -illion numbers