Principal rank plateaux in the integers beyond 10¹²

A Chinese Remainder method is developed for determining likely positive integers n starting maximal runs of size s and constant principal rank r, that is, {n + i ∈ ℤ⁺, 0 ≤ i < s : ω(n + i) = r} with ω(n − 1) ≠ r and ω(n + s) ≠ r. Instances are found for s = 2 with 9 ≤ r ≤ 59, for s = 3 with 8 ≤ r ≤ 28, for s = 4 with 7 ≤ r ≤ 18, for s = 5 with 7 ≤ r ≤ 13, and for s = 6 with 7 ≤ r ≤ 11. Several sporadic fortuitous instances are also reported.