The problem of construction of prime numbers is examined. The main lacks of the existent going are indicated near finding of prime numbers. The algorithm of construction of the system of asymmetric encipherement of RSA is considered. Dependence of the system of RSA is rotined on the rightness of finding of function of Euler. The example of determination of simplicity of number, based on the rightness of determination of finding of function of Euler, is presented. Possibility of forming of direct and reverse numbers is rotined, coming from simplicity of the checked up number. Assertion about the necessity of condition of simplicity of numbers is formulated with the use of pair of direct and reverse numbers in the great number of unzero elements of ring of Z(p-1).
prime numbers, algorithm of RSA, function of Euler, direct number, reverse number, simple factors