Large Language Models (LLMs) are widely used for question answering but are prone to hallucinations, yet the underlying causes, particularly the role of factual prevalence in training data, remain underexplored. In this work, we study this through academic authorship attribution, hypothesizing that hallucinations are more likely for less prevalent papers. Using citation count as a proxy for factual prevalence, we curate a dataset of 1.92 million papers across eight scientific disciplines with stratified samples by citation level. Experiments on three state-of-the-art LLMs confirm our hypothesis, revealing a robust inverse relationship between hallucination rate and citation count across all models and disciplines, with hallucination rates exceeding 98% for rarely cited papers and falling below 37% for highly cited ones. Our in-depth analysis further shows that these failures primarily reflect retrieval limitations rather than knowledge absence, and hidden-state probing of open-source models shows that factual prevalence is encoded in pre-generation representations, providing convergent mechanistic evidence for the prevalence-hallucination relationship.