Let's define S(k) = p₁ + p₂ + ... + p_k, i.e. "the sum of the first k primes"
The sum of the first 9 consecutive prime numbers equals 100, a square number.

Find all k (below 9999) that will similarly produce perfect squares.

(In reply to computer solution with an extension by Charlie)

A search in Sloane's OEIS, finds 9, 2474, 6694, 7785, 709838, 126789311423, (series A033997 ), giving one more value for k

Posted by Charlie on 2012-06-29 16:14:23