I'm trying to compute the rank of large, non-quadratic matrices modulo p=2,3,5 and 7.

For matrix-sizes of (approx.) 20000 x 20000 everything works fine with Rank(p,M) of LinearAlgebra[Modular].

But for (approx.) 40000 x 40000 even the parsing of the matrix is not finished after 5 days (for 20k x 20k this takes 1 or 2 hours) . The system I use has enough ram, so no swaping is involved.

First question: I expected the parsing to be O(n^2), why is this not the case?