- Not to be confused with [[:Factorization (algebra)]].
Factor is equal to 100! ≈ 9.33262154537 × 10157, where ! denotes factorial. The term was coined by Yabuszko.[1]
Decimal expansion
93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000
Etymology
The name of the number is a mix of "factorial" and nordic god "thor".
Approximations
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(9.332\times10^{157}\) | \(9.333\times10^{157}\) |
| Arrow notation | \(82\uparrow 84\) | \(10\uparrow 158\) |
| Steinhaus-Moser Notation | 82[3] | 83[3] |
| Copy notation | 8[158] | 9[158] |
| Chained arrow notation | \(82 \rightarrow 84\) | \(10 \rightarrow 158\) |
| Taro's multivariable Ackermann function | A(3,518) | A(3,519) |
| Pound-Star Notation | #*((3))*9 | #*((4))*9 |
| BEAF | {82,84} | {10,158} |
| Hyper-E notation | E[82]84 | E158 |
| Bashicu matrix system | (0)(0)(0)(0)(0)[86409] | (0)(0)(0)(0)(0)[86410] |
| Hyperfactorial array notation | 100! | |
| Fast-growing hierarchy | \(f_2(515)\) | \(f_2(516)\) |
| Hardy hierarchy | \(H_{\omega^2}(515)\) | \(H_{\omega^2}(516)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2+\omega5+7}}(10)\) | \(g_{\omega^{\omega^2+\omega5+8}}(10)\) |
Sources
- ↑ Yabuszko, Extensible ! Notation