Fish number 6

Fish number 6 (F6) is a number defined by Japanese googologist Fish in 2007. It is largest of the computable Fish numbers.

Fish function 6 uses m(m,n) map.

Definition and growth rate of Fish function 6, \(F_6(x)\), is

\begin{eqnarray*} F_6(x) &:=& m(x,2)m(x,1)(x) \\ F_6(x) &\approx& f_{\zeta_0}(x) \end{eqnarray*}

Then Fish number 6 is defined as: \[F_6 := F_6^{63}(3)\]

Therefore, Fish number 6 is greater than Fish number 5 and is approximately \(f_{\zeta_0+1}(63)\).