  Building on techniques recently introduced by the second author, and further
developed by the first author, we show that a positive integer $N$ may be
rigorously and deterministically factored into primes in at most \[ O\left(
\frac{N^{1/5} \log^{16/5} N}{(\log\log N)^{3/5}}\right) \] bit operations. This
improves on the previous best known result by a factor of $(\log \log
N)^{3/5}$.
