Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Hypothesis Gilbrayta cryptographic algorithms and data to the ACS V.L. WOLFSON Theoretical foundations of new cryptographic algorithms of information are the properties of prime numbers and reduced system of residues that are discussed in this paper. In the article the concept of convergence and convergence line indicator Gilbreath's triangle. The estimation of the line number in the triangle indicator convergence Gilbrayta. We consider the convergence of the Gilbreath's triangle when at its base are different sequences of numbers: primes in arithmetic progression, the prime numbers in the natural sequence, this system of deductions and the sieve of Eratosthenes. It is shown that the prime numbers in the natural sequence at the base of the Gilbreath's triangle occupy border position on convergence between consecutive primes in arithmetic progression and consistency of the sieve of Eratosthenes. The work consists of nine of our assertions. A consequence of the last statement is the author trying to prove the hypothesis itself Gilbrayta. Key words: prime numbers, this system of deductions, Gilbreath's hypothesis, Gilbreath's triangle, Gilbreath's Congecture triangle, the line indicator of convergence, the sieve of Eratosthenes. Contacts: Е-mail: znakvicvolf@mail.ru Pp. 06-12.