Googology Wiki
Advertisement
Googology Wiki

View full site to see MathJax equation

duodeciquingentillion is equal to \(10^{1539}\) in the short scale and \(10^{3072}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 512th -illion number.

In the long scale, \(10^{1539}\) is called sesquinquagintaducentilliard.[6]

SuperJedi224 called short-scale of this number as en-bitillion, which is equal to H(29) = H(512) = 101,539, where H(x) = 103x+3.[7]

Approximations[]

For the short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{1539}\) (exact)
Arrow notation \(10\uparrow 1539\) (exact)
Steinhaus-Moser Notation 560[3] 561[3]
Chained arrow notation \(10\rightarrow 1539\) (exact)
Taro's multivariable Ackermann function A(3,5109) A(3,5110)
BEAF & Bird's array notation {10,1539} (exact)
Hyper-E notation E1539 (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)(560) m(1)(561)
Bashicu matrix system (0)(1)[3] (0)(1)[4]
Copy notation 9[1539] 10[770]
Pound-Star Notation #*((5))*23 #*((6))*23
Hyperfactorial array notation 646! 647!
Fast-growing hierarchy \(f_2(5100)\) \(f_2(5101)\)
Hardy hierarchy \(H_{\omega^2}(5100)\) \(H_{\omega^2}(5101)\)
Slow-growing hierarchy \(g_{\omega^{\omega^3+\omega^2 5+\omega 3+9}}(10)\) (exact)

For the long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{3072}\) (exact)
Arrow notation \(10\uparrow 3072\) (exact)
Steinhaus-Moser Notation 1020[3] 1021[3]
Chained arrow notation \(10\rightarrow 3072\) (exact)
Taro's multivariable Ackermann function A(3,10201) A(3,10202)
BEAF & Bird's array notation {10,3072} (exact)
Hyper-E notation E3072 (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)(1020) m(1)(1021)
Bashicu matrix system (0)(1)[3] (0)(1)[4]
Fast-growing hierarchy \(f_2(10191)\) \(f_2(10192)\)
Hardy hierarchy \(H_{\omega^2}(10191)\) \(H_{\omega^2}(10192)\)
Slow-growing hierarchy \(g_{\omega^{\omega^3 3+\omega 7+2}}(10)\) (exact)

Sources[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-03-20.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-03-20.
  4. Fish. Conway's zillion numbers. Retrieved 2023-03-20.
  5. Fish. Conway's illion converter - 10^1539. Retrieved 2023-03-20.
  6. Fish. Conway's illion converter - 10^1539 (long scale). Retrieved 2023-03-20.
  7. -Illions - Almost Infinite

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
1,000–1030: 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
Main article: -illion
500–509: quingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
510–519: deciquingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
520–529: vigintiquingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
530–539: trigintaquingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
540–549: quadragintaquingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
550–559: quinquagintaquingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
560–569: sexagintaquingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
570–579: septuagintaquingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
580–589: octogintaquingentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
590–599: nonagintaquingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
Numbers By SuperJedi224

Fibonacci Numbers

Pound-Star Notation

Based on the Faxul

Googovipleccix family

Graham Sequence Numbers

-Illion numbers

"-Illion" numbers by SuperJedi224

Advertisement