SOLUTION: the sum of five consecutive prime numbers is even. is it true or false? and what is its counterexample?

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(39621) (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(52824) (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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