11,055 Pages

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-".

In Hyper-E notation, this is equal to E[n]1#n, and in Poly-cell notation, this is [n][n]<1>.

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 $$4^{1.34 \times 10^{154}}$$, somewhat larger than $$4^{10^{100}}$$, and concluded that "computing all [the] digits of megafuga(4) will never happen." The decimal expansion of that number begins and ends with: 23,610,226,714,597,313,206............36,860,456,095,261,392,896 However, the number is far too large to write out all of the digits.