Most everyone knows that multiplication is iterated addition and many people are aware that exponentiation is iterated multiplication. So, what is iterated exponentiation?

It’s called tetration. A tetrated stack of numbers, like the three nines in the picture, is evaluated from the top down: nine to the power of (nine to the power of nine) = 9^(9^9) or, in tetraspeak, 9^^3 (meaning 3 copies of 9 in the power tower).

In January of 2004, I published this number in decimal notation and I believe I was the first person ever to have done so. It’s not that the calculation is particularly difficult, but rather, it requires 369693100 decimal digits to fully print out and — well — most folk have better things to do with their time than that.

For comparison purposes, the currently largest known prime has only 9808358 decimal digits. There is a $100000 reward for the discovery of the first prime containing at least ten million decimal digits!