  The four-loop, two-point form factor contains the first non-planar correction
to the lightlike cusp anomalous dimension. This anomalous dimension is a
universal function which appears in many applications. Its planar part in N = 4
SYM is known, in principle, exactly from AdS/CFT and integrability while its
non-planar part has been conjectured to vanish. The integrand of the form
factor of the stress-tensor multiplet in N = 4 SYM including the non-planar
part was obtained in previous work. We parametrise the difficulty of
integrating this integrand. We have obtained a basis of master integrals for
all integrals in the four-loop, two-point class in two ways. First, we computed
an IBP reduction of the integrand of the N = 4 form factor using massive
computer algebra (Reduze). Second, we computed a list of master integrals based
on methods of the Mint package, suitably extended using Macaulay2 / Singular.
The master integrals obtained in both ways are consistent with some minor
exceptions. The second method indicates that the master integrals apply beyond
N = 4 SYM, in particular to QCD. The numerical integration of several of the
master integrals will be reported and remaining obstacles will be outlined
