The uniform primality conjecture for elliptic divisibility sequences

Let $B=(B_n)$ be an elliptic divisibility sequence generated by a rational point on an elliptic curve in minimal form. A prime term is a term $B_n/B_1$ that is prime. The uniform primality conjecture. The number of prime terms $B_n/B_1$ is uniformly bounded, independently of the curve and the point. This conjecture concerns whether elliptic divisibility sequences can contain infinitely many prime terms; the paper notes computational evidence for a gap principle and proves the conjecture conditionally in important cases, but the general assertion remains open.