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The Liber Generationis, or Συναγωγὴ χρόνων as it calls itself in the original Greek, is a short chronological account of the patriarchs, judges, and kings of Old Testament, which thence counts the years to the Nativity, the Passion, and the thirteenth year of Severus Alexander (235). In modern scholarship it is attributed to Hippolytus, martyr and “antipope” in Rome from 217 to 235, and as a result is always interpreted in terms of Hippolytus’ other written works. This article provides a wide-ranging general introduction for readers unfamiliar with this fascinating text and the evidence for it; analyses the text diachronically, on its own terms, in relation to other works of the same genre, and alongside the earliest surviving Easter table, which was indeed written by a computist named Hippolytus; and in a final appendix justifies the conclusion that neither “Hippolytus Romanus” nor this “Hippolytus the Computist”, whoever he was, composed the Synagoge.