Quinseptuagintacentillion

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A quinseptuagintacentillion is equal to \(10^{528}\) in the short scale and \(10^{1050}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4] as it is the 175th -illion number.

In the long scale, \(10^{528}\) is called octooctogintillion.

Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{528}\) (exact)
Arrow notation	\(10\uparrow 528\) (exact)
Steinhaus-Moser Notation	224[3]	225[3]
Chained arrow notation	\(10\rightarrow 528\) (exact)
Taro's multivariable Ackermann function	A(3,1750)	A(3,1751)
BEAF & Bird's array notation	{10,528} (exact)
Hyper-E notation	E528 (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)(224)	m(1)(225)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)(0)[10]	(0)(0)(0)(0)(0)(0)(0)(0)(0)[11]
Fast-growing hierarchy	\(f_2(1743)\)	\(f_2(1744)\)
Hardy hierarchy	\(H_{\omega^2}(1743)\)	\(H_{\omega^2}(1744)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 5+\omega 2+8}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{1050}\) (exact)
Arrow notation	\(10\uparrow 1050\) (exact)
Steinhaus-Moser Notation	403[3]	404[3]
Chained arrow notation	\(10\rightarrow 1050\) (exact)
Taro's multivariable Ackermann function	A(3,3485)	A(3,3486)
BEAF & Bird's array notation	{10,1050} (exact)
Hyper-E notation	E1050 (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)(403)	m(1)(404)
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Fast-growing hierarchy	\(f_2(3476)\)	\(f_2(3477)\)
Hardy hierarchy	\(H_{\omega^2}(3476)\)	\(H_{\omega^2}(3477)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3+\omega 5}}(10)\) (exact)

Sources[]

↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-16.
↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-16.
↑ Fish. Conway's zillion numbers. Retrieved 2023-02-16.

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 2023-02-16.

[3] Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-16.

[fish-4] Fish. Conway's zillion numbers. Retrieved 2023-02-16.

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