Batch sizing for convolution neural networks -- powers of 2 or powers of primes? The conventional wisdom for convolution neural networks (CNNs) is to make the batch size a power of 2 because of hardware utilization/optimizations done in the convolution layers.  

A similar logic applies to the Fast Fourier Transform (FFT). However, the FFT is actually best used when it is a size of a power of primes (e.g. $2^M3^N5^P$ where $M,N,P$ are positive integers.)  I was wondering if this also applies to CNNs.
No.  It doesn't apply to CNNs.  CNNs are doing the same operation on each item in the batch; it's much simpler than what's happening in a FFT (which involves interaction between the elements of the array; you can't compute a FFT by just separately doing something to each element of the array in parallel).