Dating Greek papyri accurately is crucial not only to edit their texts but also to understand numerous other aspects of ancient writing, document and book production and circulation, as well as various other aspects of administration, everyday life and intellectual history of antiquity. Although a substantial number of Greek papyri documents bear a date or other conclusive data as to their chronological placement, an even larger number can only be dated tentatively or in approximation, due to the lack of decisive evidence. By creating a dataset of 389 transcriptions of documentary Greek papyri, we train 389 regression models and we predict a date for the papyri with an average MAE of 54 years and an MSE of 1.17, outperforming image classifiers and other baselines. Last, we release date estimations for 159 manuscripts, for which only the upper limit is known.