Gardner on Graham's number

Pages from Martin Gardner's article on Graham's number

Graham on Graham's number

Start page from Graham & Rothschild article Page 290 from Graham & Rothschild article

F(2,n) = F(1,F(2,n-1)) = 2^F(2,n-1)
      == 2^...4 {#n-2} = 2^^n
F(3,n) = F(2,F(3,n-1)) = 2^^F(3,n-1)
      == 2^^...4 {#n-2} = 2^^^n

F(m,n) = 2^..n {^#m} = 2→n→m

a→b→c+1→2 = a→b→(a→b→c→2)
         == a→b→(..a→b→1→2.) {#c#}
          = a→b→(..a^b.) {#c#}

N* ≤ 2→3→(..12.) {#7#}
   < 4→2→8→2 == 4→2→(..16.) {#7#}

Guinness on Graham's number

Old Guinness Book of Records on Graham's number

Comments

Photo of Ron Graham juggling in the classroom

Graham's number record by Gardner:
M* ≤ 3→3→(..4.) {#64#}
   < 2→3→65→2 == 2→3→(..8.) {#64#}

Graham's original number was less:
N* ≤ 2→3→(..12.) {#7#}
   < 4→2→8→2  <  2→3→9→2