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Sum of Prime Primes

I take a prime number n. For values 1 to n, i take 1st prime no., 2nd prime no., 3rd prime no., ......., nth prime no. The number i get after addition is again prime. We know that n>5. What is the smallest value of n possible?

SOLUTION : Not Possible. Let us see how.

Except 2, all the prime numbers are odd. So, if we add prime numbers of primes, it means we are adding even number of odd numbers and an even number (n>5). This sum would always be even and greater than 2, which can never be prime. Hence, it is not possible.

e.g. if n=7, we will add 2,3,5,7,11,13,17 which has 6 odd numbers and 1 even number. The sum will be 58. You can crosscheck for other values of n as well.

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