  The paper considers the asymptotic of the ratio of the number of primes not
exceeding the primorial and the number of residues in the reduced system of
residues for the given primorial. We study the relationship between asymptotic
lower bounds for the values of the Jacobstal function and the maximum distance
between successive primes. One algorithm for computing the Jacobstal function
is given. The substantiation of the conjectures about the upper estimate of the
maximum distance between successive prime numbers is given.
