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The nth Prime Page will now find any of the first 2.623˙1015 primes or π(x) for x up to 1017.

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What is the minimum number of guests that must be invited to a party so that there are either five mutual acquaintances, or five that are mutual strangers? At least 43, but the exact number is not yet known. The solutions to this type of problem are known as Ramsey numbers, named for British mathematician Frank P. Ramsey (1903-1930).


  Submitted: 2006-08-30 21:19:58;   Last Modified: 2008-05-02 14:59:34.

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