The first chapter deals with the early history of prime number studies. It started in ancient Greece. The first ones to devote themselves to the study of prime numbers were the Pythagoreans. Their results were further developed by Euclid, whose Elements had a huge influence on all of mathematics, including prime numbers theory. We conclude our story about ancient Greek contributions to the topic with the oldest known algorithm for finding prime numbers, the Sieve of Eratosthenes. The second chapter deals with the developments in the 17th and 18th centuries. With minor exceptions, the development of the prime numbers theory was not further developed until the beginning of the 17th century. The main names for our topic in this period are de Fermat, with several contributions, of which the best known is his ’little theorem’, and Mersenne, best known for Mersenne primes, appear. The work of those two mathematicians influenced Euler, who generalised Fermat’s little theorem and expressed the law of quadratic reciprocity. Legendre and Gauß finally proved this law. In the third chapter we deal with 19th century contributions, in particular Gauß’s fundamental theorem of arithmetic and the prime number theorem. The final chapter gives a short overview of main developments concerning the best known open problems in prime number theory (Riemann’s and Goldbach’s conjecture, twin prime conjecture, …) and describes some interesting facts about prime numbers, e.g. the Ulam spiral.