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Megafuga- is a prefix used on a number n to indicate \(^nn\) using tetration (i.e. n pentated to 2). It was invented by Stephen Houben, who asked, when hearing about the fuga- prefix: Since the ^ operation is not associative, i.e. \(\left(x^yight)^z ot= x^{\left(y^zight)}\), this begs the question whether Fuga(3) means \(\left(3^3ight)^3 = 19683\) or \(3^{\left(3^3ight)} = 7625597484987\). Probably the latter, since the goal is to get big numbers.... Alistair Cockburn has kept fuga- as the former, and named the latter "megafuga-".

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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). It was invented by Stephen Houben, who asked, when hearing about the fuga- prefix: Since the ^ operation is not associative, i.e. \(\left(x^yight)^z ot= x^{\left(y^zight)}\), this begs the question whether Fuga(3) means \(\left(3^3ight)^3 = 19683\) or \(3^{\left(3^3ight)} = 7625597484987\). Probably the latter, since the goal is to get big numbers.... Alistair Cockburn has kept fuga- as the former, and named the latter "megafuga-".
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dbkwik:googology/p...iPageUsesTemplate
abstract
  • Megafuga- is a prefix used on a number n to indicate \(^nn\) using tetration (i.e. n pentated to 2). It was invented by Stephen Houben, who asked, when hearing about the fuga- prefix: Since the ^ operation is not associative, i.e. \(\left(x^yight)^z ot= x^{\left(y^zight)}\), this begs the question whether Fuga(3) means \(\left(3^3ight)^3 = 19683\) or \(3^{\left(3^3ight)} = 7625597484987\). 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 \(4^{1.34 imes 10^{153}}\), 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...
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