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Counting Prime Numbers
Some engineering folks at Google came up with a "Treasure Hunt" about a month ago, consisting of four puzzles. One new puzzle was released each week. There was probably a prize involved at some point. As far as I could tell, the purpose of the game was twofold: (1) to show off Google's new app engine; and (2) probably as a recruiting tool. Reason (2) is suspected due to the nature of the puzzles released the second and third weeks.
I particularly liked the last puzzle. It looks like the following:
I particularly liked the last puzzle. It looks like the following:
Find the smallest number that can be expressed as
the sum of 3 consecutive prime numbers,
the sum of 81 consecutive prime numbers,
the sum of 561 consecutive prime numbers,
the sum of 745 consecutive prime numbers,
and is itself a prime number.
For example, 41 is the smallest prime number that can be expressed as
the sum of 3 consecutive primes (11 + 13 + 17 = 41) and
the sum of 6 consecutive primes (2 + 3 + 5 + 7 + 11 + 13 = 41).