Question 275854
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All you need to do to prove that it is NOT true is to find a counter-example.


2 plus 3 = 5.  5 is prime.


On the other hand, if you exclude 2 by saying p and q are 2 consecutive odd primes, then the theorem is true.  Except for 2, all primes are odd and of the form *[tex \LARGE 2n\ -\ 1].  So we can say that *[tex \LARGE p\ =\ 2m\ -\ 1] and *[tex \LARGE q\ =\ 2n\ -\ 1] for some *[tex \LARGE m] and *[tex \LARGE n].


Then *[tex \LARGE p\ +\ q\ =\ 2m\ +\ 2n\ -\ 2] which is clearly an even, and therefore composite, number.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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