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Megafuga-

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Megafuga- is a prefix used on a number n to indicate \(^nn\) using tetration (i.e. n pentated to 2).[1][2] It was invented by Stephen Houben, who asked, when hearing about the fuga- prefix:

Since the ^ operation is not associative, i.e. \(\left(x^y\right)^z \not= x^{\left(y^z\right)}\), this begs the question whether Fuga(3) means \(\left(3^3\right)^3 = 19683\) or \(3^{\left(3^3\right)} = 7625597484987\). Probably the latter, since the goal is to get big numbers....

Alistair Cockburn has kept fuga- as the former, and named the latter "megafuga-".

The first five values of megafuga-x are 1, 4, 7625597484987, 108.0723*10153, and 10101.3357*102184. Houben noted, using a computer, that megafuga(4) is about \(4^{1.34 \times 10^{153}}\), somewhat larger than \(4^{10^{100}}\), and concluded that "computing all [the] digits of megafuga(4) will never happen." The leading digits of that number are: 236102267145973132...

Sources Edit

  1. A Fuga Really Big Numbers
  2. 3.2.2 - The Fz, The Fuga & The Megafuga

See also Edit

Googological affixes

Suffixes: -teen · -ty · -plex · -illion · -yllion · -chime · -toll · -gong · -bong · -throng
Prefixes: gar- · fz- · fuga- · megafuga- · booga-
SI prefixes: deca- · hecto- · kilo- · mega- · giga- · tera- · peta- · exa- · zetta- · yotta-
Obsolete SI prefixes: myria-
Extended SI prefixes: 666 · 105 · 107 · 1027 · 1030 · 1033 · 1036 · 1039 · 1042 · 1045 · 1048 · 1051 · 1054 · 1057 · 1060 · 1063 · 1090 · 10100 · 10120 · 10150 · 10180 · 10210 · 10240 · 10270 · 10300 · 10600 · 10900 · 101200 · 101500 · 101800 · 102100 · 102400 · 102700 · 103000 and higher


Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gargoogolplex
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fzhundred · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaseven · boogaeight · booganine · boogaten · boogahundred · boogagoogol · boogagoogolplex

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