Googolbang (occasionally spelled googol-bang) is equal to the factorial of a googol, \((10^{100})! \approx 10^{9.9565705518098 \times 10^{101}}\).[1][2][3] It is comparable to a googolplex; however, this is the result of raising googolplex to the 99.565705518098th power.
Its first few digits are 1,629,404,332,46... and it has exactly \(2.5 \times 10^{99} - 18\) trailing zeroes; the last non-zero digit is 6.
The exact number of digits is:
Etymology[]
The name of this number can be separated into 2 parts, "googol" and "-bang", where the suffix "-bang" means factorial operation.
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(412\uparrow972\uparrow34\) | \(107\uparrow405\uparrow39\) |
| Down-arrow notation | \(968\downarrow\downarrow35\) | \(10\downarrow\downarrow103\) |
| Steinhaus-Moser Notation | 56[3][3] | 57[3][3] |
| Copy notation | 8[8[102]] | 9[9[102]] |
| H* function | H(331H(32)) | H(332H(32)) |
| Taro's multivariable Ackermann function | A(3,A(3,337)) | A(3,A(3,338)) |
| Pound-Star Notation | #*((1))*(4,5,1,4,5)*7 | #*((1))*(5,5,1,4,5)*7 |
| BEAF | {412,{972,34}} | {107,{405,39}} |
| Hyper-E notation | E[968]34#2 \(\approx 10^{10^{101.995}}\) |
E102#2 \(= 10^{10^{102}}\) |
| Bashicu matrix system | (0)(1)[18] | (0)(1)[19] |
| Hyperfactorial array notation | (69!)! | (70!)! |
| Fast-growing hierarchy | \(f_2(f_2(332))\) | \(f_2(f_2(333))\) |
| Hardy hierarchy | \(H_{\omega^22}(332)\) | \(H_{\omega^22}(333)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^2+1}9}}(10)\) | \(g_{\omega^{\omega^{\omega^2+2}}}(10)\) |
Sources[]
See also[]
Originals: googol · googolplex
Cockburn's examples: gargoogolplex · fzgoogolplex · (mega)fugagoogolplex
Googol-n-plex: googolduplex · googoltriplex · -quadriplex · -quinplex · -sextiplex · -septiplex · -octiplex · -noniplex · -deciplex · -centiplex
Googol-103n-plex: googolmilliplex · -megaplex · -gigaplex · -teraplex · -petaplex · -exaplex · -zettaplex · -yottaplex · -xennaplex · -vekaplex · -mekaplex
Bowers' extensions: giggol · gaggol · geegol · boogol · biggol · troogol · goobol · more...
Saibian's extensions: googol-minutia · googolchime · googoltoll · googolgong · grangol · greagol · gigangol · gugold · graatagold · gugolthra · throogol · godgahlah · tethrathoth · more...
Miscellany: googolbang (10100!) · googolminex (10^-10100) · googolteen · googolty · great googol(plex) · gooprol · little googol/googolbit · zootzootplex
0-stack series: googol · googolplex · googolbang · googolplexplex · googolplexbang · googolbangplex · googolbangbang · googolplexplexplex · googolplexplexbang · googolplexbangplex · googolplexbangbang · googolbangplexplex · googolbangplexbang · googolbangbangplex · googolbangbangbang
1-stack series: googolstack · googolstackplex · googolstackbang · googolstackplexplex · googolstackplexbang · googolstackbangplex · googolstackbangbang · googolplexstack · googolplexstackplex · googolplexstackbang · googolbangstack · googolbangstackplex · googolbangstackbang · googolplexplexstack · googolplexbangstack · googolbangplexstack · googolbangbangstack
2-stack series: googolstackstack · googolstackstackplex · googolstackstackbang · googolstackplexstack · googolstackbangstack · googolplexstackstack · googolbangstackstack
3-stack series: googolstackstackstack