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Instruments and Systems: Monitoring, Control, and Diagnostics

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The research of Gilbreath's's triangle in order to develop new algorithms for encryption of information in the ACS
V.L. WOLFSON

The article presents an important question of designing process control – to ensure the confidentiality of information. The theoretical basis of the algorithm encryption of data with the public key RSA and the necessity to develop new algorithms for encryption, based on in-depth knowledge in the theory of prime numbers, and the present system of deductions.
The paper deals with one of the interesting hypotheses in the field of prime numbers – Gilbreath's problem. As the base of the triangle analyzed sufficiently wide class of sequences of natural numbers. We introduce the notion of the convergence of Gilbreath's triangle, prove several theorems about transformations of Gilbreath's triangle preserving its convergence and prove the convergence of Gilbreath's triangle. Formulate two statements for Gilbreath's triangle, the base of which is a sequence of primes, from which the proof of the conjecture.
Keywords: encryption, design, algorithm, prime numbers, Gilbreath's triangle.

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