Little graham2

This is how we solve Little Graham, 7 layers excluding the 12 arrows.

Little Graham (also called Graham-Rothschild Number[1]) is \(F^{7}(12)\), where \(F(n) = 2 \uparrow^{n} 3\) using up-arrow notation.[2] It is the original version of Graham's number. Ronald Graham published a paper[3] showing that this is an upper bound for a problem in Ramsey theory, and the number now known as Graham's number is an alternate easier-to-explain version of Little Graham. Sbiis Saibian coined the name "Little Graham", and Robert Munafo coined the name "Graham-Rothschild Number".

It is exactly \(\ [2,3,12,7]\) in the Graham Array Notation.

Two first layers of Little Graham

Below we show the dismemberment of the first two layers of Little Graham using Bower's original Hyper-Operator Notation where {n} represents exponentiation when {3}, tetration when {4}, pentation when {5}, and so on.


  1. Large Numbers (page 4) at MROB
  2. [1]
  3. Graham, R. L. and Rothschild, B. L. "Ramsey's Theorem for n-Parameter Sets." Trans. Amer. Math. Soc. 159, 257-292, 1971.
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