The library of nearrings with identity contains some surprising facts. For example that there are only few non-zerosymmetric ones or that among the 48137 nearrings on the dihedral group with 12 elements only one contains an identity. Successfully using the experience of such computer generated results, some useful necessary conditions on groups for being the additive group of a nearring with identity have been found too, thus excluding a much bigger class of groups than previously known ([13]).