How many sets of 3 or more consecutive positive odd numbers greater than 1 exist such that all of the numbers are prime?
If 2n+1, 2n+3, and 2n+5 represent three consecutive positive odd numbers greater than 1, then either 2n+1 = 3k (is a multiple of 3) or 2n+1=3k+1 => 2n+3=3k+3 (is a multiple of 3) or 2n+1=3k+2 => 2n+5=3k+6 (is a multiple of 3).
So only possibility is 3,5,7.
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Posted by Dennis
on 2006-11-08 09:25:03 |