Archimedes and Large Numbers

Archimedes was apparently intrigued by large numbers.  This is his Cattle Puzzle.

"If thou art diligent and wise, O stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacian [three-cornered] isle of Sicily, divided into four herds of different colors, one milk white, another a glossy black, a third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions: Understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all of the yellow.  . . ."

The answer contains 206,545 digits!

The first and last fifty digits of the smallest total number of cattle are 

. . . 


This problem took 22 centuries and the fastest computers to solve!

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