Human and animal memory for sequentially presented items is well-documented to be more accurate for those at the beginning and end of the sequence, phenomena known as the primacy and recency effects, respectively. By contrast, artificial neural network (ANN) models are typically designed with a memory that decays monotonically over time. Accordingly, ANNs are expected to show the recency effect but not the primacy effect. Contrary to this theoretical expectation, however, the present study reveals a counterintuitive finding: a recently developed ANN architecture, called structured state-space models, exhibits the primacy effect when trained and evaluated on a synthetic task that mirrors psychological memory experiments. Given that this model was originally designed for recovering neuronal activity patterns observed in biological brains, this result provides a novel perspective on the psychological primacy effect while also posing a non-trivial puzzle for the current theories in machine learning.