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 \(\left(3^3\right)^3 = 19,683\) or \(3^{\left(3^3\right)} = 7,625,597,484,987\). 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, 7,625,597,484,987, 108.0723*10153, and 10101.3357*102,184. 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
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