Comment by jll29

One large number that fits in 64 bits is:

  F^^^^^^F = 15 ^ .... ^ 15
  12345678
  [8*8=64 bit]

According to Conway and Guy (1996) The Book of Numbers, p. 60, the arrow notation, defined by Knuth in (1976), is such that

  m^n is  m x m x ...x m,
  m^^n is m^m^ ...^m,
  m^^^n is m^^m^^ ... ^^m,

and so on, with n copies of m in each case, and the expression being evaluated from the right.