Fermat brought us number theory(flt8)
Prime numbers are the essential elements in number theory, and the lack of easily-seen structure tends to make number theory seem ununified as a field, and its problems isolated, difficult to solve, and without clear implications to other fields of mathematics(flt8)
Gauss believed that number theory was the heart of all of mathematics(flt53)
Dirichlet proved that this progression of numbers contains infinitely many prime numbers. In his proof, Dirichlet used the field called analysis, an important area of mathematics which contains the calculus. Analysis deals with continuous things: functions on a continuum of numbers on the line, which seems very far from the discrete world of integers and prime numbers-the realm of number theory(flt60)