2^(64) -1

2^(64) -1 = 18 quintillion, 446 quadrillion, 744 trillion, 73 billion, 709 million, 551 thousand and 615

I’ve been looking for a good explanation of exponential growth.  For some reason I hadn’t realised its true power and implications, despite having it come up time and again, especially in a book like Race Against The Machine with it’s talk of being on the “second half of the chessboard.”

Well, the number above is the total number of grains of rice on a chessboard at the end of the Wheat and chessboard problem, which Wikipedia describes as:

If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?

To give an example of how things ramp up at the end of the problem:

On the 64th square of the chessboard alone there would be 263 = 9,223,372,036,854,775,808 grains of rice, or more than two billion times as much as on the first half of the chessboard.

See it all play out in this YouTube video playlist

Also see:

• Wikipedia:  Doubling time

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