A quingentillion is equal to \(10^{1503}\) in the short scale and \(10^{3000}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 500th -illion number.
In the long scale, \(10^{1503}\) is called quinquagintaducentilliard.[6]
ARsygo coined a doze pol for this number (referring to the short scale), and it is the 30th number of Vast Irregulars of Goals.[7]
Decimal expansion[]
Written out in decimal form quingentillion (in the short scale) is:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
For the short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{1503}\) (exact) | |
Arrow notation | \(10\uparrow 1503\) (exact) | |
Steinhaus-Moser Notation | 548[3] | 549[3] |
Chained arrow notation | \(10\rightarrow 1503\) (exact) | |
Taro's multivariable Ackermann function | A(3,4989) | A(3,4990) |
BEAF & Bird's array notation | {10,1503} (exact) | |
Hyper-E notation | E1503 (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)(548) | m(1)(549) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[1503] | 10[752] |
Pound-Star Notation | #*((2857))*22 | #*((2858))*22 |
PlantStar's Debut Notation | [893] | [894] |
Hyperfactorial array notation | 634! | 635! |
Strong array notation | s(10,1503) | |
Fast-growing hierarchy | \(f_2(4980)\) | \(f_2(4981)\) |
Hardy hierarchy | \(H_{\omega^2}(4980)\) | \(H_{\omega^2}(4981)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^2 5+3}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound | |
---|---|---|---|
Scientific notation | \(1\times10^{3000}\) (exact) | ||
Arrow notation | \(10\uparrow 3000\) (exact) | ||
Steinhaus-Moser Notation | 1000[3] (exact) | ||
Chained arrow notation | \(10\rightarrow 3000\) (exact) | ||
Taro's multivariable Ackermann function | A(3,9962) | A(3,9963) | |
BEAF & Bird's array notation | {10,3000} (exact) | ||
Hyper-E notation | E3000 (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)(1000) | m(1)(1001) | |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] | |
Copy notation | 9[3000] | 1[3001] | |
Pound-Star Notation | #*((2388))*30 | #*((2389))*30 | |
PlantStar's Debut Notation | [1784] | [1785] | |
Fast-growing hierarchy | \(f_2(9952)\) | \(f_2(9953)\) | |
Hardy hierarchy | \(H_{\omega^2}(9952)\) | \(H_{\omega^2}(9953)\) | |
Slow-growing hierarchy | \(g_{\omega^{\omega^3 3}}(10)\) (exact) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-03-20.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-03-20.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-03-20.
- ↑ Fish. Conway's illion converter - 10^1503. Retrieved 2023-03-20.
- ↑ Fish. Conway's illion converter - 10^1503 (long scale). Retrieved 2023-03-20.
- ↑ AR Googol - Vast Irregulars of Goals numbers Retrieved 2023-03-03.
See also[]
Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non10–19: 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
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-)