Large language models (LLMs) are known to "hallucinate" by generating false or misleading outputs. Existing hallucination benchmarks often overlook prompt sensitivity, due to stable accuracy scores despite prompt variations. However, such stability can be misleading. In this work, we introduce prompt multiplicity--the multiplicity of individual hallucinations depending on the input prompt--and study its role in LLM hallucination benchmarks. We find severe multiplicity, with even more than 50% of responses changing between correct and incorrect answers simply based on the prompt for certain benchmarks, like Med-HALT. Prompt multiplicity also gives us the lens to distinguish between randomness in generation and consistent factual inaccuracies, providing a more nuanced understanding of LLM hallucinations and their real-world harms. By situating our discussion within existing hallucination taxonomies--supporting their quantification--and exploring its relationship with uncertainty in generation, we highlight how prompt multiplicity fills a critical gap in the literature on LLM hallucinations.