A noventrigintillion or novemtrigintillion is equal to \(10^{120}\) in the short scale, or \(10^{234}\) in the long scale by Conway and Guy's naming system.by Conway-Wechsler system.[1][2][3][4][5] Noventrigintallion is an original name by Conway and novemtrigintallion is a modified name.
In the long scale which is commonly used in France and Germany, \(10^{120}\) is called vigintillion.
Aarex Tiaokhiao gave the name tetrigintillion, referring to the value of this number.[6]
Wikia user NumLynx gave the name quadragintisand for this number's short scale value.[7]
The prefix quadtena- has a meaning of one noventrigintillion[8].
In Decimal Form[]
Short scale
Long Scale
Shannon number[]
Chess opening position.
The Shannon number, named after Claude Shannon, is also equal to \(10^{120}\), and is an estimate of the game complexity of chess.[9][10] It is approximately equal to the number of possible 40 move (80 ply) games, 40 moves being a conservative estimate of the length of a chess game. It is neither the number of possible positions (estimated to be between \(10^{43}\) and \(10^{45}\)) nor the number of possible games.
Numberphile - How many chess games are possible?
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{120}\) | |
| Arrow notation | \(10\uparrow120\) | |
| Steinhaus-Moser Notation | 65[3] | 66[3] |
| Copy notation | 9[120] | 1[121] |
| Taro's multivariable Ackermann function | A(3,395) | A(3,396) |
| Pound-Star Notation | #*(9,5,5,10,4,5,6,4)*8 | #*(10,5,5,10,4,5,6,4)*8 |
| BEAF & Bird's Array Notation | {10,120} | |
| Hyper-E notation | E120 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)[5623] | (0)(0)(0)(0)(0)[5624] |
| Hyperfactorial array notation | 80! | 81! |
| Fast-growing hierarchy | \(f_2(390)\) | \(f_2(391)\) |
| Hardy hierarchy | \(H_{\omega^2}(390)\) | \(H_{\omega^2}(391)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2+\omega2}}(10)\) | |
List of prefixed numbers derived from trigintillion[]
| Name | Short scale | Long scale |
|---|---|---|
| untrigintillion | 1096 | 10186 |
| duotrigintillion | 1099 | 10192 |
| trestrigintillion | 10102 | 10198 |
| quattuortrigintillion | 10105 | 10204 |
| quintrigintillion | 10108 | 10210 |
| sestrigintillion | 10111 | 10216 |
| septentrigintillion | 10114 | 10222 |
| octotrigintillion | 10117 | 10228 |
| noventrigintillion | 10120 | 10234 |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Steve Olsen, Big-Ass Numbers
- ↑ The Conway-Wechsler System
- ↑ Extensions to the -illions I: Henkle, Conway, and Rowlett
- ↑ Fish. Conway's zillion numbers, July 25, 2021
- ↑ Aarex Tiaokhiao's illion numbers [dead link]
- ↑ NumLynx's Large Numbers
- ↑ Extension of SI prefix system by Jim Blowers (Internet archive)
- ↑ B. Blasius and R. Tönjes (2009) "Zipf's Law in the Popularity Distribution of Chess Opening" Phys. Rev. Lett. 103, 218701. doi:10.1103/PhysRevLett.103.218701 Preprint: https://arxiv.org/abs/0704.2711
- ↑ C. Shannon (1950). Programming a Computer for Playing Chess Philosophical Magazine. 41 (314)
External links[]
See also[]
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