§ 1. The primes. Factorization of a natural number m into primes § 2. The Eratosthenes sieve. Tables of prime numbers § 3. The differences between consecutive prime numbers § 4. Goldbach's conjecture § 5. Arithmetical progressions whose terms are prime numbers § 6. Primes in a given arithmetical progression § 7. Trinomial of Euler $x^2 + x + 41$ § 8. The conjecture H § 9. The function π(x) § 10. Proof of Bertrand's postulate (Theorem of Tchebycheff) § 11. Theorem of H. F. Scherk § 12. Theorem of H. E. Eichert § 13. A conjecture on prime numbers § 14. Inequalities for the function π(x) § 15. The prime number theorem and its consequences