Although it is unlikely that such an epoch-making prime factorization algorithm will actually be found, it has nothing to do with this question.

However, on closer examination, there are features of both algorithms that suggest at least a conceptual similarity. This note is written in a heuristic spirit and is intended to offer a motivation ...

The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing ...