November 2, 2640 BCE - A solar eclipse occurs around 6:25 am
October 23, 2612 BCE - a solar eclipse occurs around 6:22 am
The moon in both of these cases is 0% illuminated according to Sky Safari Plus version 6. Possibly also providing an explanation for Keku (the god of darkness) to be the second born son. The 2612 BCE date is slightly more likely due to it being closer to the expected Sothic Cycle dates. The 2640 BCE date falls an extra couple of days outside of expectations.