  We compute the integrands of five-, six-, and seven-point correlation
functions of twenty-prime operators with general polarizations at the two-loop
order in N=4 super Yang-Mills theory. In addition, we compute the integrand of
the five-point function at three-loop order. Using the operator product
expansion, we extract the two-loop four-point function of one Konishi operator
and three twenty-prime operators. Two methods were used for computing the
integrands. The first method is based on constructing an ansatz, and then
numerically fitting for the coefficients using the twistor-space reformulation
of N=4 super Yang-Mills theory. The second method is based on the OPE
decomposition. Only very few correlator integrands for more than four points
were known before. Our results can be used to test conjectures, and to make
progresses on the integrability-based hexagonalization approach for correlation
functions.
