Determinism conjecture for the generalized Cullen number primality algorithm

Let $b$ and $n$ be positive integers, and let the algorithm described in the paper test the generalized Cullen number $C_b(n)$. The algorithm is called deterministic when every tested generalized Cullen prime is certified as such and the output PRIME NUMBER guarantees primality.

Determinism conjecture. If

$$n>b,$$

then the algorithm is deterministic.

The algorithm is otherwise only quasi-deterministic: a PRIME NUMBER output certifies that the tested integer is prime, but the algorithm might fail to certify a generalized Cullen prime. Computational evidence reported in the paper suggests that such primes occur only when $n<b$, and that the auxiliary value $K$ used in step 3 is small relative to $n$.