2786! is approximately equal to \(10^{3.4677786446 \times 10^{130}}\). This number is given in Robert Munafo's Notable Properties of Specific Numbers as an example of a calculation that can be performed easily using Hypercalc.[1] It is also the the number shown as default in the input line of HyperCalc Javascript.[2]
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(223\uparrow781\uparrow45\) | \(544\uparrow20\uparrow100\) |
| Down-arrow notation | \(19\downarrow\downarrow103\) | \(673\downarrow\downarrow47\) |
| Steinhaus-Moser Notation | 69[3][3] | 70[3][3] |
| Copy notation | 3[3[131]] | 4[4[131]] |
| H* function | H(11H(42)) | H(12H(42)) |
| Taro's multivariable Ackermann function | A(3,A(3,432)) | A(3,A(3,433)) |
| Pound-Star Notation | #*((1))*(4,3,3,0,2,3)*7 | #*((1))*(5,3,3,0,2,3)*7 |
| BEAF | {223,{781,45}} | {544,{20,100}} |
| Hyper-E notation | E[19]102#2 | E[673]46#2 |
| Bashicu matrix system | (0)(1)[20] | (0)(1)[21] |
| Hyperfactorial array notation | (84!)! | (85!)! |
| Fast-growing hierarchy | \(f_2(f_2(426))\) | \(f_2(f_2(427))\) |
| Hardy hierarchy | \(H_{\omega^22}(426)\) | \(H_{\omega^22}(427)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^2+\omega3}3}}(10)\) | \(g_{\omega^{\omega^{\omega^2+\omega3}4}}(10)\) |