39 (read as "to-the-third-nine") is a positive integer equal to \(9^{9^{9}} = 9^{387,420,489} \approx 4.281247731757470 \times 10^{369,693,099}\). It has 369,693,100 digits. The superscript represents tetration. It is also called Ulysses Number.[1]
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(4.281\times10^{369\,693\,099}\) | \(4.282\times10^{369\,693\,099}\) |
| Arrow notation | \(9\uparrow\uparrow3\) | |
| Steinhaus-Moser Notation | 8[3][3] | 9[3][3] |
| Copy notation | 3[3[9]] | 4[4[9]] |
| Taro's multivariable Ackermann function | A(3,A(3,27)) | A(3,A(3,28)) |
| Pound-Star Notation | #*((1))*6798 | #*((1))*6799 |
| BEAF | {9,3,2} | |
| Hyper-E notation | E[9]1#3 | |
| Bashicu matrix system | (0)(1)[5] | (0)(1)[6] |
| Hyperfactorial array notation | (11!)! | (12!)! |
| Fast-growing hierarchy | \(f_2(f_2(25))\) | \(f_2(f_2(26))\) |
| Hardy hierarchy | \(H_{\omega^22}(25)\) | \(H_{\omega^22}(26)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^\omega}}(9)\) | |