On a conjecture of Pomerance and the role of Jacobsthal function

In 1980, Pomerance conjectured that if $k$ is a positive integer such that the first $\phi(k)$ primes co-prime to $k$ form a reduced residue system mod$k$, then $k \leq 30.$ This conjecture is still open. We shall discuss some old and new results towards this conjecture and how the Jacobsthal function plays an important role in this problem.