Leave-One-Out Stable Conformal Prediction (LOO-StabCP) is introduced as an efficient method for predictive uncertainty quantification, improving upon the computational limitations of traditional conformal prediction methods. By utilizing leave-one-out stability, LOO-StabCP significantly accelerates prediction requests and demonstrates enhanced performance on both synthetic and real-world datasets, particularly in screening applications. The method is theoretically grounded and outperforms existing techniques like split conformal in terms of test power.