Googolillion (or decitriotriacontillion) is an "-illionized" version of the googol, equal to \(10^{3\left(10^{100}\right)+3}\) in the American system.[1] This number is also equal to 106*10100 in the long scale of naming zillions, accepted in French and Germany.
Approximations
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(1000\uparrow(1+10\uparrow100)\) | |
| Down-arrow notation | \(50\downarrow\downarrow60\) | \(368\downarrow\downarrow40\) |
| Steinhaus-Moser Notation | 56[3][3] | 57[3][3] |
| Copy notation | 2[2[101]] | 3[3[101]] |
| H* function | H(10H(32)) | |
| Taro's multivariable Ackermann function | A(3,A(3,332)) | A(3,A(3,333)) |
| Pound-Star Notation | #*((1))*(8,1,8,3)*10 | #*((1))*(8,5,3,5,4)*7 |
| BEAF | {1000,1+{10,100}} | |
| Hyper-E notation | E(3+3E100) | |
| Bashicu matrix system | (0)(1)[331] | (0)(1)[332] |
| Hyperfactorial array notation | (69!)! | (70!)! |
| Fast-growing hierarchy | \(f_2(f_2(327))\) | \(f_2(f_2(328))\) |
| Hardy hierarchy | \(H_{\omega^22}(327)\) | \(H_{\omega^22}(328)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^2}3+3}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \((10\uparrow6)\uparrow(10\uparrow100)\) | |
| Down-arrow notation | \(735\downarrow\downarrow36\) | \(892\downarrow\downarrow35\) |
| Steinhaus-Moser Notation | 56[3][3] | 57[3][3] |
| Copy notation | 5[5[101]] | 6[6[101]] |
| H* function | H(19H(32)) | H(20H(32)) |
| Taro's multivariable Ackermann function | A(3,A(3,333)) | A(3,A(3,334)) |
| Pound-Star Notation | #*((1))*(5,1,4,6,4)*7 | #*((1))*(11,10,6,1)*11 |
| BEAF | {{10,6},{10,100}} | |
| Hyper-E notation | E(6E100) | |
| Bashicu matrix system | (0)(1)[332] | (0)(1)[333] |
| Hyperfactorial array notation | (69!)! | (70!)! |
| Fast-growing hierarchy | \(f_2(f_2(328))\) | \(f_2(f_2(329))\) |
| Hardy hierarchy | \(H_{\omega^22}(328)\) | \(H_{\omega^22}(329)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^2}6}}(10)\) | |
Sources
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 · trevigint · quattuorvigint · quinvigint · sexvigint · septenvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
40–49: quadragintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
50–59: quinquagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
80–89: octogintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
100–900: centillion · unviginticent · ducent · trecent · duotrigintatrecent · quadringent · quingent · sescent · septuagintisescent · septingent · octingent · nongent
1,000–1024: millillion · dumill · trimill · quadrimill · quinmill · sexmill · septimill · octimill · nonimill · myr · centimill · micr · nan · pic · femt · att · zept · yoct
