Euclid Theorem.

     The set of the prime numbers is infinite.

     Proof. Let's assume, the multitude of prime number and A prime numbers is finite. Let P be the greatest - number A+1 is greater the product of all prime numbers from 2 to P. The than any prime numberthus must be divisible , hence, it must be composite and by some prime the primes, also is q. Otherwise, A, itself, as a product of all divisible by must be divisible by q. But then the difference (A+1) - A = 1 also qthe quantity of the , but that is impossible. Gotten contradiction proves that prime numbers is infinite, what was to be proved.