Mega


 * Not to be confused with mega-.

Mega is equal to Circle(2) or Pentagon(2) in Steinhaus-Moser notation. Steinhaus showed that it is equal to Square(256):


 * Pentagon(2) = Square(Square(2)) = Square(Triangle(Triangle(2))) = Square(Triangle(4)) = Square(256)

Matt Hudelson calls it zelda. In his version of Steinhaus-Moser notation, it is denoted Triangle(2). Mega can also be defined recursively as \(m_{256}\) in the sequence defined by \(m_0 = 256\) and \(m_{n + 1} = m_n^{m_n}\).

Mega can be bounded in arrow notation as:

\[10\uparrow\uparrow 257 < \text{Mega} < 10\uparrow\uparrow 258\]

It can be bounded more precisely in Hyper-E notation:

\[\text{E}619\#256 < \text{Mega} < \text{E}620\#256\]

It is therefore between giggol and giggolplex.

The last digits of mega are ...93539660742656. Calculating the last digits of the mega is harder than calculating the last digits of Graham's number because the "base" of exponentiation in the mega keeps changing when the triangles are applied, which results in a more complex behavior.

It is the last number listed on Robert Munafo's Notable Properties of Specific Numbers.

Mega can be expressed as M(2,3) in Hyper-Moser Notation.