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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[]

  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.
  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.

See also[]

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
1,000–1024: 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
Main article: -illion
700–709: septingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
710–719: deciseptingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
720–729: vigintiseptingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
730–739: trigintaseptingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
740–749: quadragintaseptingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
750–759: quinquagintaseptingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
760–769: sexagintaseptingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
770–779: septuagintaseptingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
780–789: octogintaseptingentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
790–799: nonagintaseptingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
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