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The first lucky prime. Since lucky numbers are lucky enough to repeatedly appear in this book, let's take a moment to define them. Start with the list of natural numbers: 1, 2, 3, ... , and cross out every second number. The second number not crossed out is 3, so we cross out every third number, leaving 1, 3, 7, 9, 13, 15, .... The third number left is 7, so we cross out every seventh number---repeat forever. What remains is the sequence of lucky numbers: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, .... S. Ulam (1909-1984) investigated these numbers and found a strong resemblance to primes.

 

  Submitted: 2008-03-03 17:48:59;   Last Modified: 2009-12-05 00:53:42.



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