Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of a positive integer N in N2/9+o(1) bit operations. Prior to this breakthrough, the best known complexity bound for this problem was N1/4+o(1)
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, a result going back to the 1970s. In this paper we push Hittmeir's techniques further, obtaining a rigorous, deterministic factoring algorithm with complexity