We survey and update data on runs of consecutive integers each having exactly r distinct prime factors (briefly, of principal rank r). For 3 ≤ r ≤ 64 and other sporadic values, lower bounds are given for the size of longest runs of consecutive integers of principal rank r, together with upper bounds on the first occurrence of such runs. We also prove that there are infinitely many pairs of consecutive integers of principal rank r, for each r ≥ 3.
Bulletin of the Institute of Combinatorics and its Applications Vol. 64, p. 30-38