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The Paul Erd\H{o}s-Tur\'an inequality is used as a quantitative form of Weyl's criterion, together with other criteria to asses equidistribution propertieson some patterns of sequences that arise from indexation of prime numbers,Jumping Champions (called here and in previous work, "meta-distances" or evenmd, for short). A statistical meta-analysis is also made of previous researchconcerning meta-distances to review the conclusion that meta-distances can becalled Low-discrepancy sequences (LDS), and thus exhibiting another numericalevidence that md's are an equidistributed sequence. Ramanujan's master theoremis used to conjecture that the types of integrands where md's can be used moresuccesfully for quadratures are product-related, as opposite toaddition-related. Finally, it is conjectured that the equidistribution of md'smay be connected to the know equidistribution of zeros of Riemann's zetafunction, and yet still have enough "information" for quasi-random integration("right" amount of entropy).

On the equidistribution properties of patterns in prime numbers Jumping  Champions, metaanalysis of properties as Low-Discrepancy Sequences, and some  conjectures based on Ramanujan's master theorem and the zeros of Riemann's  zeta function