Primality conjecture for generalized elliptic Fermat numbers

Let $E$ be a fixed elliptic curve over $\mathbb{Q}$, let $P\in E(\mathbb{Q})$ be a rational point, and let $m$ be the fixed integer indexing the generalized elliptic Fermat numbers $F=(F_k^{(m)}(E,P))_{k\in\mathbb{N}}$. Primality conjecture for generalized elliptic Fermat numbers. The sequence $F$ contains only finitely many prime terms. This extends the preceding primality question from elliptic Fermat numbers to generalized elliptic Fermat numbers; no resolution of the stated claim is supplied in the given text.