Conjecture that minimal-base cardinalities form an interval for primitive groups

Let $G$ be a primitive permutation group on a domain $\Omega$, and let $\mathcal{M}(G,\Omega)$ denote the set of cardinalities of minimal bases of $G$ on $\Omega$. Primitive interval conjecture. The set $\mathcal{M}(G,\Omega)$ is an interval of natural numbers.

The conjecture reflects the absence of known primitive examples for which the set of minimal-base cardinalities is not an interval. It concerns the structure of minimal bases in primitive permutation groups; the source reports only computational evidence and no additional confirmation.