As far as My knowledge is concern, the largest number known is rayo's number even it is greater than graham's number (G64). but what actually rayo's number is? How can we know the value of it.
@Peter
By replacing "Googol" with any positive integer we can get a rayo(n).
I know it is uncomputable and not possible to compute by a turing Machine .
But i want to feel this number.
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I remember I was discussing this same problem with one of my friends and how the computers are improving year after year. The computation of much larger numbers than those we could find even 10 years ago are possible by different available programs. But, still we have to look into future. For now, I Magma and Gap to compute the largest known numbers. I haven't tried our programs such as Maple. For example, do you remember how we used use scientific calculators to write very large numbers in Scientific Notations like 7.34 X 10^100? And of course we accepted them, but we can use some program like Magma and compute all the digits of the same exact number.
So I suggest writing a program on Magma or Maple or Gap and compare the two numbers Rayo's number with Breuer's number. I suggest asking Dr. John Cannon in Sydney Australia. He is an expert in writing this kind of programs.
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