Diophantine Inequalities as a Problem of Difference between Consecutive Primes

In the present paper, we have developed a method for solving $\mathit{\text{diophantine}}\mathit{\text{inequalities}}$ using their relationship with the $\mathit{\text{difference}}\mathit{\text{between}}\mathit{\text{consecutive}}\mathit{\text{primes}}$. 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.