Consecutive numbers in multiplication tables

A multiplication table of size x is the set of all possible products a · b with 1 ≤ a, b ≤ √x. In this article, we study the number of pairs of consecutive integers in a multiplication table and obtain non-trivial lower and upper bounds of its size. For multiplication rectangle with side lengths x0.088 and x0.912, we obtain an almost optimal asymptotic, showing evidence of independence of integers lying in multiplication tables.