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We demonstrate how radio pulsars can be used as random number generators. Specifically, we focus on publicly verifiable randomness (PVR), in which the same sequence of trusted and verifiable random numbers is obtained by multiple parties. PVR is a critical building block for many processes and algorithms (including cryptography, scientific trials, electoral audits and international treaties). However, current approaches (based on number theory) may soon become vulnerable to quantum computers, motivating a growing demand for PVR based on natural physical phenomena. In this context, we explore pulsars as a potential physical PVR source. We first show that bit sequences extracted from the measured flux densities of a bright millisecond pulsar can pass standardised tests for randomness. We then quantify three illustrative methods of bit-extraction from pulsar flux density sequences, using simultaneous observations of a second pulsar carried out with the Parkes telescope in Australia and the Five-hundred-metre Aperture Spherical radio Telescope (FAST) in China, supported by numerical simulations. We demonstrate that the same bit sequence can indeed be obtained at both observatories, but the ubiquitous presence of radiometer noise needs to be accounted for when determining the expected bit error rate between two independent sequences. We discuss our results in the context of an imaginary use-case in which two mutually distrusting parties wish to obtain the same random bit sequence, exploring potential methods to mitigate against a malicious participant.