The arithmetic function \(g(n)\) of Jacobsthal is defined as the least positive integer such that every sequence of \(g(n)\) consecutive integers contains at least one member which is prime to \(n\). It is proved for all \(k\geq 1\) that \[ g(n)\leq 2k^{2+2e\log k}, \] where \(k\) is the number of distinct primes dividing \(n\).