  In the present paper, we have developed a method for solving
\textit{diophantine inequalities} using their relationship with the
\textit{difference between consecutive primes}.
  Using this approach we have been able to prove some theorems, including
Ingham's exponential theorem as well as some new results. Diophantine
inequalities and their connection with Cramer's and Andrica's conjectures are
also discussed.
