- Not to be confused with trecentillion.
A trescentillion is equal to \(10^{312}\) in the short scale and \(10^{618}\) in the long scale by Conway and Guy's naming system.[1][2][3][4] Jonathan Bower called this number centretillion.[5]
In the modified Conway system, \(10^{312}\) is called trecentillion. Meauk pointed out that trecentillion has 2 meanings of \(10^{312}\) and \(10^{903}\) in the modified Conway system.[6] Because of that, Fish claims that using the modified Conway system is discouraged.[4]
In the long scale, \(10^{312}\) is called duoquinquagintillion.
Approximations[]
For short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{312}\) | |
Arrow notation | \(10\uparrow312\) | |
Steinhaus-Moser Notation | 144[3] | 145[3] |
Copy notation | 9[312] | 1[313] |
Chained arrow notation | \(10→312\) | |
H* function | H(103) | |
Taro's multivariable Ackermann function | A(3,1033) | A(3,1034) |
Pound-Star Notation | #*((844))*11 | #*((845))*11 |
BEAF | {10,312} | |
Hyper-E notation | E312 | |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)[74989] | (0)(0)(0)(0)(0)(0)[74990] |
Bird's array notation | {10,312} | |
Hyperfactorial array notation | 172! | 173! |
Strong array notation | s(10,312) | |
Fast-growing hierarchy | \(f_2(1026)\) | \(f_2(1027)\) |
Hardy hierarchy | \(H_{\omega^2}(1026)\) | \(H_{\omega^2}(1027)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^23+\omega+2}}(10)\) |
For long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{618}\) | |
Arrow notation | \(10\uparrow618\) | |
Steinhaus-Moser Notation | 256[3] | 257[3] |
Copy notation | 9[618] | 1[619] |
Chained arrow notation | \(10\rightarrow618\) | |
H* function | H(205) | |
Taro's multivariable Ackermann function | A(3,2049) | A(3,2050) |
Pound-Star Notation | #*((485))*15 | #*((486))*15 |
BEAF | {10,618} | |
Hyper-E notation | E618 | |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[67317] | (0)(0)(0)(0)(0)(0)(0)[67318] |
Hyperfactorial array notation | 301! | 302! |
Fast-growing hierarchy | \(f_2(2041)\) | \(f_2(2042)\) |
Hardy hierarchy | \(H_{\omega^2}(2041)\) | \(H_{\omega^2}(2042)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^26+\omega+8}}(10)\) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-07.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-07.
- ↑ 4.0 4.1 Fish. Conway's zillion numbers. Retrieved 2023-02-07.
- ↑ Illion Numbers
- ↑ Meauk's tweet
See also[]
Main article: -illion
100–109: centillion (un- · duo- · tres- · quattuor- · quin- · sex- · septen- · octo- · noven-)110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
120–129: viginticentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
140–149: quadragintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
150–159: quinquagintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
180–189: octogintacentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)