  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 properties
on some patterns of sequences that arise from indexation of prime numbers,
Jumping Champions (called here and in previous work, "meta-distances" or even
md, for short). A statistical meta-analysis is also made of previous research
concerning meta-distances to review the conclusion that meta-distances can be
called Low-discrepancy sequences (LDS), and thus exhibiting another numerical
evidence that md's are an equidistributed sequence. Ramanujan's master theorem
is used to conjecture that the types of integrands where md's can be used more
succesfully for quadratures are product-related, as opposite to
addition-related. Finally, it is conjectured that the equidistribution of md's
may be connected to the know equidistribution of zeros of Riemann's zeta
function, and yet still have enough "information" for quasi-random integration
("right" amount of entropy).
