An uncentillion, cenuntillion, centummillion[1] or cebillion as named by Aarex Tiaokhiao,[2] is equal to \(10^{306}\)[3] in short scale, and \(10^{606}\) in long scale. It is the largest -illion expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).
Approximations[]
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{306}\) | |
| Arrow notation | \(10\uparrow306\) | |
| Steinhaus-Moser Notation | 142[3] | 143[3] |
| Copy notation | 9[306] | 1[307] |
| Taro's multivariable Ackermann function | A(3,1013) | A(3,1014) |
| Pound-Star Notation | #*((437))*11 | #*((438))*11 |
| BEAF | {10,306} | |
| Hyper-E notation | E306 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[60429] | (0)(0)(0)(0)(0)(0)[60430] |
| Hyperfactorial array notation | 169! | 170! |
| Fast-growing hierarchy | \(f_2(1\,006)\) | \(f_2(1\,007)\) |
| Hardy hierarchy | \(H_{\omega^2}(1\,006)\) | \(H_{\omega^2}(1\,007)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^23+6}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{606}\) | |
| Arrow notation | \(10\uparrow606\) | |
| Steinhaus-Moser Notation | 252[3] | 253[3] |
| Copy notation | 9[606] | 1[607] |
| Taro's multivariable Ackermann function | A(3,2010) | A(3,2011) |
| Pound-Star Notation | #*((187))*15 | #*((188))*15 |
| BEAF | {10,606} | |
| Hyper-E notation | E606 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[54246] | (0)(0)(0)(0)(0)(0)(0)[54247] |
| Hyperfactorial array notation | 296! | 297! |
| Fast-growing hierarchy | \(f_2(2\,002)\) | \(f_2(2\,003)\) |
| Hardy hierarchy | \(H_{\omega^2}(2\,002)\) | \(H_{\omega^2}(2\,003)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^26+6}}(10)\) | |
Sources[]
See also[]
Standard -centillion numbers 10303 (10600)
Main article: -illion
100–109: centillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
120–129: viginticentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
140–149: quadragintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
150–159: quinquagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
180–189: octogintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)