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Consecutive Odd and Prime (Posted on 2006-11-08) Difficulty: 1 of 5
How many sets of 3 or more consecutive positive odd numbers greater than 1 exist such that all of the numbers are prime?

See The Solution Submitted by Richard    
Rating: 2.2500 (4 votes)

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a solution | Comment 1 of 4

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
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