Sum of Sequence of Squares of Primes

Theorem
Let $S = \left\langle{s_n}\right\rangle$ be the integer sequence defined as:


 * $\displaystyle s_n = \sum_{i \mathop = 1}^n {p_i}^2$

where $P_i$ denotes the $i$th prime number.

Then $S$ begins:
 * $4, 13, 38, 87, 208, 377, 666, 1027, 1556, 2397, 3358, 4727, 6408, 8257, 10466, \ldots$