Realizing personalized medicine at scale calls for methods that distill insights from longitudinal patient journeys, which can be viewed as a sequence of medical events. Foundation models pretrained on large-scale medical event data represent a promising direction for scaling real-world evidence generation and generalizing to diverse downstream tasks. Using Epic Cosmos, a dataset with medical events from de-identified longitudinal health records for 16.3 billion encounters over 300 million unique patient records from 310 health systems, we introduce the Curiosity models, a family of decoder-only transformer models pretrained on 118 million patients representing 115 billion discrete medical events (151 billion tokens). We present the largest scaling-law study of medical event data, establishing a methodology for pretraining and revealing power-law scaling relationships for compute, tokens, and model size. Consequently, we pretrained a series of compute-optimal models with up to 1 billion parameters. Conditioned on a patient's real-world history, Curiosity autoregressively predicts the next medical event to simulate patient health timelines. We studied 78 real-world tasks, including diagnosis prediction, disease prognosis, and healthcare operations. Remarkably for a foundation model with generic pretraining and simulation-based inference, Curiosity generally outperformed or matched task-specific supervised models on these tasks, without requiring task-specific fine-tuning or few-shot examples. Curiosity's predictive power consistently improves as the model and pretraining scale. Our results show that Curiosity, a generative medical event foundation model, can effectively capture complex clinical dynamics, providing an extensible and generalizable framework to support clinical decision-making, streamline healthcare operations, and improve patient outcomes.