Subexponential algorithms in general have long had proven running times. Dixon's method [1], in particular, has had a proven running time since 1980. The number

Subexponential algorithms in general have long had proven running times. Dixon's method [1], in particular, has had a proven running time since 1980. The number field sieve itself has had some recent progress on that front [2]. However, those algorithms are _probabilistic_, not _deterministic_, which is what sets this linked method apart. This algorithm, much like Pollard-Strassen before it, is pretty much irrelevant to integer factorization in practice. But it is nevertheless remarkable to see some progress on deterministic factorization after such a long time. [1] https://doi.org/10.1090/S0025-5718-1981-0595059-1 https://doi.org/10.1090/S0025-5718-1981-0595059-1 [2] https://doi.org/10.1016/j.jnt.2017.10.019 https://doi.org/10.1016/j.jnt.2017.10.019