“…The error term magnitude in the theorem above has been obtained by relying on estimations by Balazard [1], Bordèlles [3], El-Marraki [6], Helfgott [8, §6] and Ramaré [15], [16], among others; nonetheless, when using non-explicit tools, one should expect an error of magnitude e −w √ log(U ) for some constant w > 0. Furthermore, in order to derive Theorem 1, one must abandon the classical prime-number-theorem-like approach (as in [7], for example), as it gives ineffective estimations, or explicit that involve huge numbers, and thus are inconvenient or impractical.…”