Pretraining language models directly on web-scale corpora is the de facto paradigm. We study an alternative where the model is initially exposed to abstract structured data to ease the subsequent acquisition of rich semantic knowledge, much like humans learning simple logic and mathematics before higher reasoning. We focus on procedural data, generated by formal languages and other simple algorithms, as such abstract data. We first diagnose the algorithmic skills that different forms of procedural data can improve, often significantly. For example, the accuracy of context recall (Needle-in-a-haystack) jumps from 10 to 98% when a model is pretrained on Dyck sequences (balanced brackets). Second, we study how these gains are reflected in pretraining larger models (up to 1.3B). We find that front-loading as little as 0.1 to 0.3% procedural data significantly outperforms standard pretraining on natural language, code, and informal mathematics (C4, CodeParrot, and DeepMind-Math datasets). Notably, this also enables the models to reach the same loss value with only 55/67/86% of the original data and thus a comparable reduction in FLOPs. Third, we explore the mechanisms behind the benefits and find that procedural pretraining instills non-trivial structure in both attention and MLP layers. The former is particularly important for structured domains (e.g. code), and the latter for language. Finally, we lay a path for combining multiple forms of procedural data. Our results show that procedural pretraining is a simple, lightweight means of improving performance and accelerating language model pretraining, ultimately suggesting the promise of disentangling knowledge acquisition from reasoning in LLMs.