Towards the QED beta function and renormalons at 1=N2f and 1=N3.

We determine the 1=N2 f and 1=N3 f contributions to the QED beta function stemming from the closed set of nested diagrams. At the order of 1=N2 f, we discover a new logarithmic branch cut closer to the origin when compared to the 1=Nf results. The same singularity location appears at 1=N3 f, and these correspond to a UV renormalon singularity in the finite part of the photon two-point function