Computational language models (LMs), most notably exemplified by the widespread success of OpenAI's ChatGPT chatbot, show impressive performance on a wide range of linguistic tasks, thus providing cognitive science and linguistics with a computational working model to empirically study different aspects of human language. Here, we use LMs to test the hypothesis that languages with more speakers tend to be easier to learn. In two experiments, we train several LMs – ranging from very simple n-gram models to state-of-the-art deep neural networks – on written cross-linguistic corpus data covering 1,294 different languages and statistically estimate learning difficulty. Using a variety of quantitative methods and machine learning techniques to account for phylogenetic relatedness and geographical proximity of languages, we show that there is robust evidence for a relationship between learning difficulty and speaker population size. However, contrary to expectations derived from previous research, our results suggest that languages with more speakers tend to be harder to learn.