One of the error codes of ARPACK roughly maps to this condition:

NCV-NEV >= 2 and less than or equal to N.

Where NCV is the number of lanczos vectors you are allowed to use and NEV is the number of eigenvalues.

Now from simple math, NCV <= N means that NCV – NEV >= 2 <=> NEV <= NCV – 2 <= N – 2

But an NxN matrix would have N eigenvalues, so it seems ARPACK will always miss two eigenvalues? If I understand things properly?