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Inquisitive questions — open-ended, curiosity-driven questions people ask as they read — are an integral part of discourse processing and comprehension. Recent work in NLP has taken advantage of question generation capabilities of LLMs to enhance a wide range of applications. But the space of inquisitive questions is vast: many questions can be evoked from a given context. So which of those should be prioritized to find answers? Linguistic theories have not yet provided an answer. This paper presents QSALIENCE, a salience predictor of inquisitive questions. QSALIENCE is instruction-tuned over a dataset of linguist-annotated salience scores of 1,766 (context, question) pairs. A question scores high on salience if answering it would greatly enhance the understanding of the text. The authors show that highly salient questions are empirically more likely to be answered in the same article, bridging potential questions with Questions Under Discussion. They further validate their findings by showing that answering salient questions is an indicator of summarization quality in news.