Fast Algorithms
For the implementation of a "fast" algorithm (similar to how FFT computes the DFT), it is often desirable that the transform length is also highly composite, e.g. a power of two. However, there are specialized fast Fourier transform algorithms for finite fields, such as Wang and Zhu's algorithm, which are efficient regardless of whether the transform length factors.
Read more about this topic: Discrete Fourier Transform (general)
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“The universe constantly and obediently answers to our conceptions; whether we travel fast or slow, the track is laid for us. Let us spend our lives in conceiving then. The poet or the artist never yet had so fair and noble a design but some of his posterity at least could accomplish it.”
—Henry David Thoreau (1817–1862)