Blindness affects millions of people around the world, and is expected to become increasingly prevalent in the years to come. For some blind individuals, a promising solution to restore a form of vision are cortical visual prostheses, which convert camera input to electrical stimulation of the cortex to bypass part of the impaired visual system. Due to the constrained number of electrodes that can be implanted, the artificially induced visual percept (a pattern of localized light flashes, or 'phosphenes') is of limited resolution, and a great portion of the field's research attention is devoted to optimizing the efficacy, efficiency, and practical usefulness of the encoding of visual information. A commonly exploited method is the non-invasive functional evaluation in sighted subjects or with computational models by making use of simulated prosthetic vision (SPV) pipelines. Although the SPV literature has provided us with some fundamental insights, an important drawback that researchers and clinicians may encounter is the lack of realism in the simulation of cortical prosthetic vision, which limits the validity for real-life applications. Moreover, none of the existing simulators address the specific practical requirements for the electrical stimulation parameters. In this study, we developed a PyTorch-based, fast and fully differentiable phosphene simulator. Our simulator transforms specific electrode stimulation patterns into biologically plausible representations of the artificial visual percepts that the prosthesis wearer is expected to see. The simulator integrates a wide range of both classical and recent clinical results with neurophysiological evidence in humans and non-human primates. The implemented pipeline includes a model of the retinotopic organisation and cortical magnification of the visual cortex. Moreover, the quantitative effect of stimulation strength, duration, and frequency on phosphene size and brightness as well as the temporal characteristics of phosphenes are incorporated in the simulator. Our results demonstrate the suitability of the simulator for both computational applications such as end-to-end deep learning-based prosthetic vision optimization as well as behavioural experiments. The modular approach of our work makes it ideal for further integrating new insights in artificial vision as well as for hypothesis testing. In summary, we present an open-source, fully differentiable, biologically plausible phosphene simulator as a tool for computational, clinical and behavioural neuroscientists working on visual neuroprosthetics.