Computational Evidence for a Conjecture in Number Theory

We present computational evidence supporting the following conjecture: For any integer n >= 2, let P_n be the set of primes of the form k^2 + 1 where 1 <= k <= n. Let S_n be the sum of these primes. The conjecture states that S_n is never a perfect power (i.e., S_n != x^a for integers x > 1, a > 1), with the single exce. An exhaustive search over 50,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.