We have proposed that the abiogenesis of life around the beginning of the Archean may have been an example of “spontaneous” microscopic dissipative structuring of UV-C pigments under the prevailing surface ultraviolet solar spectrum. The thermodynamic function of these Archean pigments (the “fundamental molecules of life”), as for the visible pigments of today, was to dissipate the incident solar light into heat. We have previously described the non-equilibrium thermodynamics and the photochemical mechanisms which may have been involved in the dissipative structuring of the purines adenine and hypoxanthine from the common precursor molecules of hydrogen cyanide and water under this UV light. In this article, we extend our analysis to include the production of the other two important purines, guanine and xanthine. The photochemical reactions are presumed to occur within a fatty acid vesicle floating on a hot (∼80 °C) neutral pH ocean surface exposed to the prevailing UV-C light. Reaction–diffusion equations are resolved under different environmental conditions. Significant amounts of adenine (∼10−5 M) and guanine (∼10−6 M) are obtained within 60 Archean days, starting from realistic concentrations of the precursors hydrogen cyanide and cyanogen (∼10−5 M).