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## Vynnychuk S., Maksymenko E.

The way for accelerating Fermat’s method of numbers factorization was offered due to the decimation of trial values of unknown X using a set of the bases of the module in which the essential role belongs to the allocated basic basis of the bb module. The basic basis is selected from the condition of maximum bb relationship to the number of those Xmodbb, for which the difference X2 – N is a quadratic residue by mod bb (permissible Xmodbb) and available RAM of computer. Based on bb the list of steps of variable length between the the nearest largest permissible Xmodbb is formed. The algorithm of MR realizing the decimation of trial values is described. For the most frequently performed steps of the algorithm of MR the fragment of a program code in language C is presented. The results of numerical experiments for the decomposition of numbers on the factors which are the product of two primes such that the ratio of highest to lowest does not exceed 4. It is shown that using only the decimation procedure of trial values, the time expenses in solving the problem of decomposition into factors is always proportional to the number (p + q)/2 – N1/2, where N = pq. They significantly depend on the choice of the basic basis of the module and a set of other bases of modules.