- Not to be confused with pentahectillion.
Pentehectillion is equal to \(10^{3\cdot10^{315} + 3}\).[1][2] It is defined using Sbiis Saibian's generalization of Jonathan Bowers' -illion system.
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(1000\uparrow(1+10\uparrow315)\) | |
| Down-arrow notation | \(1000\downarrow\downarrow106\) | \(937\downarrow\downarrow107\) |
| Steinhaus-Moser Notation | 144[3][3] | 145[3][3] |
| Copy notation | 2[2[316]] | 3[3[316]] |
| H* function | H(H(104)) | |
| Taro's multivariable Ackermann function | A(3,A(3,1046)) | A(3,A(3,1047)) |
| Pound-Star Notation | #*((1))*((2))*9 | #*((1))*((3))*9 |
| BEAF | {1000,1+{10,315}} | |
| Hyper-E notation | E(3+3E315) | |
| Bashicu matrix system | (0)(1)[32] | (0)(1)[33] |
| Hyperfactorial array notation | (172!)! | (173!)! |
| Fast-growing hierarchy | \(f_2(f_2(1039))\) | \(f_2(f_2(1040))\) |
| Hardy hierarchy | \(H_{\omega^22}(1039)\) | \(H_{\omega^22}(1040)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^23+\omega+5}3+3}}(10)\) | |