Question 1179725: the sum of five consecutive prime numbers is even. is it true or false? and what is its counterexample?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! 2, 3, 5, 7, 11 ------one even number and four odd numbers. Sum is even.
3, 5, 7, 11, 13 ------odd number of odd numbers. Sum is odd.
That should be clear enough.
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
It is not always true.
It is false sometime.
It is true in one and only one case: if the first of five consecutive prime numbers is 2.
Otherwise, it is FALSE: as a counter-example, consider the sequence of five consecutive primes 3, 5, 7, 11, 13 with the sum of 39.
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