  We consider the ordered sequence of coprimes to a given primorial number and
investigate differences between consecutive elements. The Jacobsthal function
applied to the concerning primorial turns out to represent the greatest of
these differences. We will explore the smallest even number which does not
occur as such a difference. Little is known about even natural numbers below
the respective Jacobsthal function which cannot be represented as a difference
between consecutive numbers coprime to a primorial. Existence and frequency of
these numbers have not yet been clarified. Using the relation between
restricted coverings of sequences of consecutive integers and the occuring
differences, we derive a bound below which all even natural numbers are
differences between consecutive numbers coprime to a given primorial $p_k\#$.
Furthermore, we provide exhaustive computational results on non-existent
differences for primes $p_k$ up to $k=44$. The data suggest the assumption that
all even natural numbers up to $h(k-1)$ occur as differences of coprimes to
$p_k\#$ where $h(n)$ is the Jacobsthal function applied to $p_n\#$.
