In this paper we discuss the effect of background pressure and synthesis temperature on the graphene crystal sizes in chemical vapor deposition (CVD) on copper catalyst. For the first time, we quantitatively demonstrate a fundamental role of the background pressure and provide the activation energy for graphene nucleation in atmospheric pressure CVD (9 eV), which is substantially higher than for the low pressure CVD (4 eV). We attribute the difference to a greater importance of copper sublimation in the low pressure CVD, where severe copper evaporation likely dictates the desorption rate of active carbon from the surface. At atmospheric pressure, where copper evaporation is suppressed, the activation energy is assigned to the desorption energy of carbon clusters instead. The highest possible temperature, close to the melting point of copper, should be used for large single crystal graphene synthesis. Using these conditions, we have synthesized graphene single crystals with sizes over 0.5 mm. Single cry