We show that n-bit integers can be factorized by independently running a quantum circuit with O~(n3/2) gates for n−−√+4 times, and then using polynomial-time classical post-processing. The correctness of the algorithm relies on a number-theoretic heuristic assumption reminiscent of those used in subexponential classical factorization algorithms. It is currently not clear if the algorithm can lead to improved physical implementations in practice.