  We investigate the signature of primordial non-Gaussianities in the weak
lensing bispectrum, in particular the signals generated by local, orthogonal
and equilateral non-Gaussianities. The questions we address include the
signal-to-noise ratio generated in the Euclid weak lensing survey (we find the
1sigma-errors for fNL are 200, 575 and 1628 for local, orthogonal and
equilateral non-Gaussianities, respectively), misestimations of fNL if one
chooses the wrong non-Gaussianity model (misestimations by up to a factor of
+/-3 in fNL are possible, depending on the choice of the model), the
probability of noticing such a mistake (improbably large values for the
chi^2-functional occur from fNL 200 on), degeneracies of the primordial
bispectrum with other cosmological parameters (only the matter density Omega_m
plays a significant role), and the subtraction of the much larger,
structure-formation generated bispectrum. If a prior on a standard
wCDM-parameter set is available from Euclid and Planck, the structure formation
bispectrum can be predicted accurately enough for subtraction, and any residual
structure formation bispectrum would influence the estimation of fNL to a minor
degree. Configuration-space integrations which appear in the evaluation of
chi^2-functionals and related quantities can be carried out very efficiently
with Monte-Carlo techniques, which reduce the complexity by a factor of O(10^4)
while delivering sub-percent accuracies. Weak lensing probes smaller scales
than the CMB and hence provide an additional constraint on non-Gaussianities,
even though they are not as sensitive to primordial non-Gaussianities as the
CMB.
