The Primakoff process plays a crucial role in axion productionin astrophysical environments and laboratories. Given the rising interestin axion physics and many on-going experimental activities, we conducta comprehensive calculation of this process and carefully examineseveral aspects that have been neglected in the literature. In particular,our calculation is valid for axions with significantly large masses,which would be of importance to axion searches utilizing crystal andliquid xenon detectors. We present the most updated calculation ofthe Primakoff solar axion flux, with a simple parametrization thatis applicable to a broad range of axion masses up to a few tens ofkeV. Our code is publicly available at GitHub.