  We solve some famous conjectures on the distribution of primes. These
conjectures are to be listed as Legendre's, Andrica's, Oppermann's, Brocard's,
Cram\'{e}r's, Shanks', and five Smarandache's conjectures. We make use of both
Firoozbakht's conjecture (which recently proved by the author) and Kourbatov's
theorem on the distribution of and gaps between consecutive primes. These
latter conjecture and theorem play an essential role in our methods for proving
these famous conjectures. In order to prove Shanks' conjecture, we make use of
Panaitopol's asymptotic formula for $\pi(x)$ as well.

General Mathematics