Enigma 1122: Chapter and worse
26 March 2017
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From New Scientist #2278, 17th February 2001 [link]
While waiting for a much-delayed train, George found himself trying to read a very boring book. He soon gave up and started counting its pages instead. Chapter 1 started on Page 1, and each subsequent chapter started at the top of a page. The boredom factor was enhanced by the fact that the length in pages of each chapter was equal to the chapter number multiplied by the length of Chapter 1.
With still no sign of the train, George proceeded to total all the page numbers in each chapter. Again, the totals for each chapter were exact multiples of the total for Chapter 1, but this time the multiples did not equate to chapter numbers. For the last chapter the multiple was a prime number, even though the chapter number was not.
How many pages were there in the book?