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. 

Posted by Dennis on 2006-11-08 09:25:03