This work is concerned with maximal and currently obtained fill factors of crystalline silicon solar cells. Recent research activities has led to a drastically decreased recombination in the volume and at the surfaces of crystalline silicon solar cells. As a result, the reported open-circuit voltages (Voc) and fill factor (FF) values increased significantly. In order to classify how good the achieved improvements are, it is necessary to know the maximum fill factor (FFmax) achievable for a certain open circuit voltage. Thus, in this work we calculate FFmax-Voc-pairs for an ideal resistance free single junction silicon solar cell limited by intrinsic recombination only as a function of dopant concentration and thickness by using state-of-the art analytical models. The obtained curves are compared to recently published record FF-Voc-pairs showing that all currently published record FF-Voc-pairs stay below this limit. For calculating FFmax-Voc-pairs we provide a simple extension of Green' well known FF0-equation.