Quattuorvigintiducentillion

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A quattuorvigintiducentillion is equal to \(10^{675}\) in the short scale and \(10^{1344}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4]^[5] as it is the 224th -illion number.

In the long scale, \(10^{675}\) is called duodecicentilliard.

Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{675}\) (exact)
Arrow notation	\(10\uparrow 675\) (exact)
Steinhaus-Moser Notation	276[3]	277[3]
Chained arrow notation	\(10\rightarrow 675\) (exact)
Taro's multivariable Ackermann function	A(3,2239)	A(3,2240)
BEAF & Bird's array notation	{10,675} (exact)
Hyper-E notation	E675 (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)(276)	m(1)(277)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)(0)[20]	(0)(0)(0)(0)(0)(0)(0)(0)(0)[21]
Fast-growing hierarchy	\(f_2(2231)\)	\(f_2(2232)\)
Hardy hierarchy	\(H_{\omega^2}(2231)\)	\(H_{\omega^2}(2232)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 6+\omega 7+5}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{1344}\) (exact)
Arrow notation	\(10\uparrow 1344\) (exact)
Steinhaus-Moser Notation	498[3]	499[3]
Chained arrow notation	\(10\rightarrow 1344\) (exact)
Taro's multivariable Ackermann function	A(3,4461)	A(3,4462)
BEAF & Bird's array notation	{10,1344} (exact)
Hyper-E notation	E1344 (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)(498)	m(1)(499)
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Fast-growing hierarchy	\(f_2(4452)\)	\(f_2(4453)\)
Hardy hierarchy	\(H_{\omega^2}(4452)\)	\(H_{\omega^2}(4453)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3+\omega^2 3+\omega 4+4}}(10)\) (exact)

Sources[]

↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-21.
↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-21.
↑ Fish. Conway's zillion numbers. Retrieved 2023-02-21.
↑ Fish. Conway's illion converter - 10^675. Retrieved 2023-02-21.

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 -ducentillion numbers 10⁶⁰³ (10¹²⁰⁰)

Main article: -illion

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

[2] Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-21.

[3] Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-21.

[fish-4] Fish. Conway's zillion numbers. Retrieved 2023-02-21.

[5] Fish. Conway's illion converter - 10^675. Retrieved 2023-02-21.

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