Phigol is equal to \(\lfloor 10^{99}\phi \rfloor\), or the first 100 digits of \(\phi\) without the decimal point.[1] Its full decimal expansion is:
Its prime factorization is 3 × 8,342,699,992,611,683 × 200,346,780,527,216,943,982,143,179,768,801,147 × 322,683,969,787,780,736,862,368,046,487,637,814,725,351,618,779.
Approximations
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1.618\times10^{99}\) | \(1.619\times10^{99}\) |
| Arrow notation | \(55\uparrow57\) | \(180\uparrow44\) |
| Steinhaus-Moser Notation | 56[3] | 57[3] |
| Copy notation | 1[100] | 2[100] |
| Taro's multivariable Ackermann function | A(3,326) | A(3,327) |
| Pound-Star Notation | #*(1,3,4,9,2,5,1)*9 | #*(11,7,10,8,7,3)*11 |
| BEAF | {55,57} | {180,44} |
| Hyper-E notation | E99 | 2E99 |
| Bashicu matrix system | (0)(0)(0)(0)(0)[1259] | (0)(0)(0)(0)(0)[1260] |
| Bird's array notation | {55,57} | {180,44} |
| Hyperfactorial array notation | 69! | 70! |
| Strong array notation | s(55,57) | s(180,44) |
| Fast-growing hierarchy | \(f_2(321)\) | \(f_2(322)\) |
| Hardy hierarchy | \(H_{\omega^2}(321)\) | \(H_{\omega^2}(322)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega2+4}6}(31)\) | \(g_{\omega^{\omega+16}4}(44)\) |
Sources
See also
Hypermathematics: bigoogol · trigoogol · quadrigoogol · coogol(plex)
Hyperlicious: wakoogol(plex) · wakamoogol(plex) · wonkapoogol(plex) · ultron
Numbers with a W: woogol · wiggol · waggol · weegol · wigol · woggol · wagol · bwoogol · bwiggol · bwaggol · bweegol · bwigol · bwoggol · bwagol
Primes: Gooprol · Booprol · Trooprol · Quadrooprol
Other: Bentley's Number · Pigol · Egol · Phigol · gongol(plex) · kaboodol(plex) · gaz(illion)