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A prime number generator for devices for noise-resistant transmission of information along a radio channel. (English. Russian original) Zbl 0883.11005
Dokl. Math. 52, No. 1, 135-137 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 343, No. 6, 749-751 (1995).
A matrix recursion for the generation of prime numbers is studied. The equation is of the form: $A_i^{(N_k )} = \left[ A_n^{(N_k )} P_{k-1} + B_i^{(N_k )} N_k \right]\pmod{P_k}$ where $$N_k$$ is the $$k$$-th prime number, $$P_k = \prod_{m=1}^k N_m$$, $$A_n^{(N_k )}$$ is a matrix of dimension $$(N_k -1) \cdot (N_{k-1} -1)$$ and $$B_i^{(N_k )}$$ is a matrix of dimension $$(N_k -1) \times (N_{k-1} -1)$$. The matrices $$A_i^{(N_k )}$$ are viewed as initial elements of another recursion and its properties are studied. It is shown, in particular, that all the elements of these matrices $$A_i^{(N_k )}$$ that are less than $$N_{k+1}^2$$ are primes if the product $$P_k$$ contains all the prime numbers from $$1$$ to $$N_k$$.
##### MSC:
 11A41 Primes 94A99 Communication, information 11Y11 Primality
##### Keywords:
matrix recursion; generation of prime numbers