Pseudoprime Numbers: Basic Concepts and the Problem of Security
نویسنده
چکیده
The analysis of existing methods of construction of prime numbers is carried out in the presented paper. New concepts related to pseudoprime numbers are introduced. Theorems are formulated and proved on the basis of which such numbers are constructed. Using pseudoprime numbers can significantly reduce the number of candidates viewed as primes. The proposed corollaries of the theorems allow to significantly increase the ranges of unambiguous determination of such candidates. The results of the conducted experiments are presented, their analysis is carried out. The most important result of applying pseudoprime numbers is the estimation of the number of numbers to be checked. For large numbers with a size of more than 200 decimal signs, they make up less than 8 percent of the numbers on a given interval, and as the size of the numbers increases, this percentage decreases. Based on experimental data, basic properties of pseudoprime numbers are formulated.
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