  Jacobsthal's conjecture has been disproved by counterexample a few years ago.
We continue to verify this conjecture on a larger scale. For this purpose, we
implemented an extension of the Greedy Permutation Algorithm and computed the
maximum Jacobsthal function for the product of $k$ primes up to $k=43$. We have
found various new counterexamples. Their pattern seems to imply that the
conjecture of Jacobsthal only applies to several small $k$. Our results raise
further questions for discussion. In addition to this paper, we provide
exhaustive information about all covered sequences of the appropriate maximum
lengths in ancillary files.
