I am trying to find gaussian primes using the method outlined in this answer: https://stackoverflow.com/questions/2269810/whats-a-nice-method-to-factor-gaussian-integers
Using the Julia programming language and I am able to find k for the following equality up to p = 233. Here k = 3, which results in the following gaussian primes: 8+13i & 13+8i
mod(mod(BigInt(k)^((p - 1) / 2), p), p) == mod(-1, p)
However, I am unable to find $k$ for the next prime $p = 241?$