The odd-prime occurrence conjecture for full Collatz processes

Let $f$ be the Collatz function and let $\{f^{s}(b)\}_{s=1}^{\infty}$ be a full Collatz process. The odd-prime occurrence conjecture. There exists an odd prime $p$ such that

$$p\in\{f^{s}(b)\}_{s=1}^{\infty}.$$

The paper presents this as another conjectural primality property of full Collatz processes. The supplied text gives no resolution evidence.