20,523
pages

View full site to see MathJax equation

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:

995,657,055,180,967,481,723,488,710,810,833,949,177,056,029,941,963,334,338,855,462,168,341,353,507,911,292,252,707,750,506,615,682,568

## 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

Googol and related numbers

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

Googol plex bang stack numbers