Septingentillion

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A septingentillion is equal to \(10^{2103}\) in the short scale and \(10^{4200}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4]^[5] as it is the 700th -illion number.

In the long scale, \(10^{2103}\) is called quinquagintatrecentilliard.^[6]

Decimal expansion[]

In the short scale:

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In the long scale:

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Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{2103}\) (exact)
Arrow notation	\(10\uparrow 2103\) (exact)
Steinhaus-Moser Notation	733[3]	734[3]
Chained arrow notation	\(10\rightarrow 2103\) (exact)
Copy notation	9[2103]	10[1052]
Taro's multivariable Ackermann function	A(3,6983)	A(3,6984)
BEAF & Bird's array notation	{10,2103} (exact)
Hyper-E notation	E2103 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(9)\)	\(s(1)^3(\lambda x.x+1)(10)\)
m(n) map	m(1)(733)	m(1)(734)
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Fast-growing hierarchy	\(f_2(6973)\)	\(f_2(6974)\)
Hardy hierarchy	\(H_{\omega^2}(6973)\)	\(H_{\omega^2}(6974)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3 2+\omega^2+3}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{4200}\) (exact)
Arrow notation	\(10\uparrow 4200\) (exact)
Steinhaus-Moser Notation	1342[3]	1343[3]
Chained arrow notation	\(10\rightarrow 4200\) (exact)
Copy notation	9[4200]	1[4201]
Taro's multivariable Ackermann function	A(3,13949)	A(3,13950)
BEAF & Bird's array notation	{10,4200} (exact)
Hyper-E notation	E4200 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(10)\)	\(s(1)^3(\lambda x.x+1)(11)\)
m(n) map	m(1)(1342)	m(1)(1343)
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Fast-growing hierarchy	\(f_2(13938)\)	\(f_2(13939)\)
Hardy hierarchy	\(H_{\omega^2}(13938)\)	\(H_{\omega^2}(13939)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3 4+\omega^2 2}}(10)\) (exact)

Sources[]

↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-05-11.
↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-05-11.
↑ Fish. Conway's zillion numbers. Retrieved 2023-05-11.
↑ Fish. Conway's illion converter - 10^2103. Retrieved 2023-05-11.
↑ Fish. Conway's illion converter - 10^2103 (long scale). Retrieved 2023-05-11.

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 -septingentillion numbers 10²¹⁰³ (10⁴²⁰⁰)

Main article: -illion

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

[2] Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-05-11.

[3] Olsen, Steve. Big-Ass Numbers. Retrieved 2023-05-11.

[fish-4] Fish. Conway's zillion numbers. Retrieved 2023-05-11.

[5] Fish. Conway's illion converter - 10^2103. Retrieved 2023-05-11.

[6] Fish. Conway's illion converter - 10^2103 (long scale). Retrieved 2023-05-11.

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