Question 181675
A student claims that every prime greater than 3 is a term in the arithmetic sequence who nth term is 6n+1 or in the arithmetic sequence whose nth term is 6n-1. Is this true? If so why?
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Look at those two arithmetic sequences:

The arithmetic sequence whose nth term is 6n+1 is 7,13,19,25,31,37,...

The arithmetic sequence whose nth term is 6n-1 is 5,11,17,23,29,35,...

One of the other of those two progressions contains every odd number
greater than 3, which is not a multiple of 3.  And since every prime 
number greater than 3 is odd, and is not a multiple of 3, it must be 
true for every prime number greater than 3.

Quod Erat Demonstrandum

Edwin</pre>