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Digital Dice by Paul J. Nahin

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4. A Curious Coin-Flipping Game

In 1876 Edouard Lucas (remember him from Problem 1?) showed indirectly that 267 — 1 could not, as had been conjectured since the early 1600s, be a prime number. Lucas could not, however, actually factor this enormous number. Then, in 1903, the American mathematician Frank Cole (1861–1926) gave a remarkable paper at a meeting of the American Mathematical Society. Without saying a word, he walked to the blackboard and calculated 267— 1. Then he multiplied out, longhand,

 

193,707,721 × 761,838,257,287.

 

The two calculations ...

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