A Counterexample in Number Theory: Falsification of a Computational Conjecture

We report the falsification of the following conjecture: The count of primes of the form n^2+1 up to a given bound is asymptotically equal to 2*C*Li(x) where C is a constant approximately 0.685 and Li(x) is the logarithmic integral, with the constant C being related to the product over odd primes of (1-1/(. A counterexample was discovered computationally: witness = (50000, 37, 3538). This result was obtained by the SOVEREIGN autonomous research system.