 Vinogradov Type I–II method

This method uses cancellation in Type I sums and Type II sums to control a sum weighted by the Von Mangoldt function. The Vaughan identity separates the short-factor contributions from bilinear ones. Fourier separation of interval cutoffs permits a hyperbolic product cutoff. Ben Green's 2007 notes, Sections 2.3–2.4 give a version adapted to binary digit sums.