Aims.In this paper we aim to determine the longest pulsation period of infrared carbon stars. Methods: .Forty-seven infrared carbon stars were selected based on (1) IRAS colours and spectral classification from the IRAS LRS atlas, and (2) known carbon stars with large CO expansion velocities. Multi-epoch JHKL'photometry was obtained. Results: .Reliable periods could be derived for 31 stars. The two longest periods are 840 and 870 days, only slightly longer than the previously longest known period for a galactic carbon star of 783 days. This is considerably shorter than the periods of some OH/IR stars. As the present survey targeted carbon stars that are likely to be among those with the longest periods expected, this difference appears real. To try to understand the longest observed period, the synthetic AGB code of Wagenhuber & Groenewegen (1998, A&A, 340, 183) was fine-tuned to reproduce the models of Vassiliadis & Wood (1993, ApJ, 413, 641). For several initial masses the fundamental mode period distribution was calculated for stars inside observed instability strip. Depending on details of the adopted mass loss rate, it is found that the mass limit where a carbon star has a probability of less than 1% of being in the observed instability strip with a period longer than 900 days is between 2.6 and 3.1 M&sun;. Conclusions: .Synthetic AGB calculations suggest that the observed upper limit in period can be interpreted as an upper mass limit of carbon star formation, with a value of between 2.6 and 3.1 M&sun;, depending on the adopted AGB mass loss rate. Such a mass limit is predicted by stellar evolution through the occurence of Hot Bottom Burning where (dredged-up) carbon is converted into nitrogen; this is predicted to occur at higher masses (~4 M&sun;), although this depends on convection and core overshoot.