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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 E102#2
Bashicu matrix system (0)(1)[336] (0)(1)[337]
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

  1. Googol - Cantor's Attic
  2. googol-bang
  3. Notable Properties of Specific Numbers (page 21)

See also

Googol plex bang stack numbers

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