Octoquinquagintacentillion

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An octoquinquagintacentillion is equal to \(10^{477}\) in the short scale and \(10^{948}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4] as it is the 158th -illion number.

In the long scale, \(10^{477}\) is called novenseptuagintilliard.

Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{477}\) (exact)
Arrow notation	\(10\uparrow 477\) (exact)
Steinhaus-Moser Notation	206[3]	207[3]
Chained arrow notation	\(10\rightarrow 477\) (exact)
Taro's multivariable Ackermann function	A(3,1581)	A(3,1582)
BEAF & Bird's array notation	{10,477} (exact)
Hyper-E notation	E477 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(7)\)	\(s(1)^3(\lambda x.x+1)(8)\)
m(n) map	m(1)(206)	m(1)(207)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)[72]	(0)(0)(0)(0)(0)(0)(0)(0)[73]
Fast-growing hierarchy	\(f_2(1573)\)	\(f_2(1574)\)
Hardy hierarchy	\(H_{\omega^2}(1573)\)	\(H_{\omega^2}(1574)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 4+\omega 7+7}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{948}\) (exact)
Arrow notation	\(10\uparrow 948\) (exact)
Steinhaus-Moser Notation	369[3]	370[3]
Chained arrow notation	\(10\rightarrow 948\) (exact)
Taro's multivariable Ackermann function	A(3,3146)	A(3,3147)
BEAF & Bird's array notation	{10,948} (exact)
Hyper-E notation	E948 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(8)\)	\(s(1)^3(\lambda x.x+1)(9)\)
m(n) map	m(1)(369)	m(1)(370)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)(0)[71]	(0)(0)(0)(0)(0)(0)(0)(0)(0)[72]
Fast-growing hierarchy	\(f_2(3137)\)	\(f_2(3138)\)
Hardy hierarchy	\(H_{\omega^2}(3137)\)	\(H_{\omega^2}(3138)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 9+\omega 4+8}}(10)\) (exact)

Sources[]

↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-14.
↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-14.
↑ Fish. Conway's zillion numbers. Retrieved 2023-02-14.

See also[]

Standard -illion numbers 10³ⁿ⁺³ (10⁶ⁿ)

Main article: -illion

1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non
10–19: decillion · undec · duodec · tredec · quattuordec · quindec · sexdec · septendec · octodec · novemdec
20–29: vigintillion · unvigint · duovigint · tresvigint · quattuorvigint · quinvigint · sesvigint · septemvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
40–49: quadragintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
50–59: quinquagintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
80–89: octogintillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
100–900: centillion · ducent · trecent · quadringent · quingent · sescent · septingent · octingent · nongent
1,000–10³⁰: millillion · dumill · dumillinonagintanongent · trimill · trimilliduotrigintatrecent · trimillisexoctogintaoctingent · quadrimill · quadrimilliquattuordecicent · quinmill · sexmill · septimill · octimill · nonimill · myr · decimilliquinsexagintasescent · dumyr · unquadragintamilliunquinquagintacent · centimill · micr · nan · pic · femt · att · zept · yoct · ront · quect

Standard -centillion numbers 10³⁰³ (10⁶⁰⁰)

Main article: -illion

[1] Conway and Guy. (1995) "The book of Numbers" Copernicus

[2] Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-14.

[3] Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-14.

[fish-4] Fish. Conway's zillion numbers. Retrieved 2023-02-14.

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