Centillion

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For Aarex's centillion, see novenonagintillion.

A centillion is equal to 10³⁰³ in the short scale, or 10⁶⁰⁰ in the long scale.^[1]^[2] It is also equal to googolty³. It is the largest -illion with a name that is in the standard English dictionary^[3], 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 (10^3x+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^[4], Aarex Tiaokhiao named it cemillion, referring to the value of this number.^[5] BlankEntity named it Ceegol.^[6] Russ Rowlett's Greek-based naming system of zillions names it hectahenillion.^[7]

Written out in decimal form centillion (in the short scale) is:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

In long scale:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Approximations[]

For short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{303}\)
Arrow notation	\(10\uparrow303\)
Steinhaus-Moser Notation	\(140[3]\)	\(141[3]\)
Copy notation	\(9[303]\)	\(10[152]\)
Chained arrow notation	\(10\rightarrow303\)
Taro's multivariable Ackermann function	\(A(3,1003)\)	\(A(3,1004)\)
Pound-Star Notation	\(\#\text{}((314))\text{}11\)	\(\#\text{}((315))\text{}11\)
BEAF	\(\{10,303\}\)
Hyper-E notation	\(\textrm{E}303\)
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	\(\{10,303\}\)
Hyperfactorial array notation	\(168!\)	\(169!\)
Strong array notation	\(\textrm{s}(10,303)\)
Fast-growing hierarchy	\(f_2(996)\)	\(f_2(997)\)
Hardy hierarchy	\(H_{\omega^2}(996)\)	\(H_{\omega^2}(997)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^{2}3+3}}(10)\)

For long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{600}\)
Arrow notation	\(10\uparrow600\)
Steinhaus-Moser Notation	\(250[3]\)	\(251[3]\)
Copy notation	\(9[600]\)	\(1[601]\)
Chained arrow notation	\(10→600\)
Taro's multivariable Ackermann function	\(A(3,1990)\)	\(A(3,1991)\)
Pound-Star Notation	\(\#((116))15\)	\(\#((117))15\)
BEAF	\(\{10,600\}\)
Hyper-E notation	\(\textrm{E}600\)
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	\(\{10,600\}\)
Hyperfactorial array notation	\(294!\)	\(295!\)
Strong array notation	\(\textrm{s}(10,600)\)
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	\(g_{\omega^{\omega^{2}6}}(10)\)