Centillion

A centillion is equal to 10303 in the short scale, or 10600 in the long scale.Conway and Guy. The Book of Numbers. Copernicus. 1995. ISBN 978-0387979939 p.16Centillion at Wolfram MathWorld It is also equal to googolty3. It is the largest -illion with a name that is in the standard English dictionaryMerriam-webster Dictionary. Centillion, and considered to be the second-largest standard number found in most major English dictionaries (the only larger number in the standard English dictionary is the googolplex, and the third-largest standard number found in most English dictionaries being googol). It is 304 digits long in the short scale, or 601 digits long in the long scale. In the long scale, 10303 is called quinquagintilliard.
The name is derived from the French word "cent", meaning one hundred and the -illion suffix (103x+3). It is number one followed by 303 zeroes, with a total of 101 commas and it is 304 digits long. Its total of 101 commas is the only two large numbers in English with more than 100 commas (the other being googolplex).
The short scale version of this number is exactly equal to one thousand times (reasonably close by googological standards) googol3 and the long scale version is exactly equal to googol6.
For the short scale version, Sbiis Saibian names it eceton; it is E303 in his notation, Aarex Tiaokhiao named it cemillion, referring to the value of this number.Aarex Tiaokhiao's illion numbers BlankEntity named it Ceegol.BlankEntity's Googology Site Russ Rowlett's Greek-based naming system of zillions names it hectahenillion.Russ Rowlett's Greek Based -illions
Written out in decimal form centillion (in the short scale) is:
In long scale:
==Approximations==
For short scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{303}\) 	\(1\times10^{303}\)
Arrow notation 	\(10\uparrow303\) 	\(10\uparrow303\)
Steinhaus-Moser Notation 	\(140[3]\) 	\(141[3]\)
Copy notation 	\(9[303]\) 	\(10[152]\)
Chained arrow notation 	\(10\rightarrow303\) 	\(10\rightarrow303\)
Taro's multivariable Ackermann function	\(A(3,1003)\) 	\(A(3,1004)\)
Pound-Star Notation 	\(\#\text{*}((314))\text{*}11\) 	\(\#\text{*}((315))\text{*}11\)
BEAF 	\(\{10,303\}\) 	\(\{10,303\}\)
Hyper-E notation 	\(\textrm{E}303\) 	\(\textrm{E}303\)
s(n) map 	\(s(1)^2(\lambda x.x+1)(996)\) 	\(s(1)^2(\lambda x.x+1)(997)\)
m(n) map 	m(1)(140) 	m(1)(141)
Bashicu matrix system 	\((0)(0)(0)(0)(0)(0)[54246]\) 	\((0)(0)(0)(0)(0)(0)[54247]\)
Bird's array notation 	\(\{10,303\}\) 	\(\{10,303\}\)
Hyperfactorial array notation 	\(168!\) 	\(169!\)
Strong array notation 	\(\textrm{s}(10,303)\) 	\(\textrm{s}(10,303)\)
Fast-growing hierarchy 	\(f_2(996)\) 	\(f_2(997)\)
Hardy hierarchy 	\(H_{\omega^2}(996)\) 	\(H_{\omega^2}(997)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^{2}3+3}}(10)\)	\(g_{\omega^{\omega^{2}3+3}}(10)\)
For long scale:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{600}\) 	\(1\times10^{600}\)
Arrow notation 	\(10\uparrow600\) 	\(10\uparrow600\)
Steinhaus-Moser Notation 	\(250[3]\) 	\(251[3]\)
Copy notation 	\(9[600]\) 	\(1[601]\)
Chained arrow notation 	\(10→600\) 	\(10→600\)
Taro's multivariable Ackermann function	\(A(3,1990)\) 	\(A(3,1991)\)
Pound-Star Notation 	\(\#*((116))*15\) 	\(\#*((117))*15\)
BEAF 	\(\{10,600\}\) 	\(\{10,600\}\)
Hyper-E notation 	\(\textrm{E}600\) 	\(\textrm{E}600\)
s(n) map 	\(s(1)^3(\lambda x.x+1)(7)\) 	\(s(1)^3(\lambda x.x+1)(8)\)
m(n) map 	m(1)(250) 	m(1)(251)
Bashicu matrix system 	\((0)(0)(0)(0)(0)(0)(0)[48696]\)	\((0)(0)(0)(0)(0)(0)(0)[48697]\)
Bird's array notation 	\(\{10,600\}\) 	\(\{10,600\}\)
Hyperfactorial array notation 	\(294!\) 	\(295!\)
Strong array notation 	\(\textrm{s}(10,600)\) 	\(\textrm{s}(10,600)\)
Fast-growing hierarchy 	\(f_2(1\,982)\) 	\(f_2(1\,983)\)
Hardy hierarchy 	\(H_{\omega^2}(1\,982)\) 	\(H_{\omega^2}(1\,983)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^{2}6}}(10)\)	\(g_{\omega^{\omega^{2}6}}(10)\)
== Sources ==
== See also ==
* Ecetonplex
* Duocentillion
* Ducentillion
* Vigintillion
fr:Centillion
ja:センティリオン
zh:Centillion
Category:Numbers
Category:Illion
Category:Class 2
Category:Eceton series
Category:Powers of 10 with squarefree exponent
Category:Numbers with 101 to 999 digits
Category:Tier 1 -illion numbers
Category:Googol—grangol series
Category:Numbers with peer-reviewed source