Getting formulas for the extraction of all prime numbers from the Pascal's triangle

The following arithmetic study presents previously unknown numerical properties of the Pascal's right-angled triangle and gives the main results of finding its real discriminant for the first time. Precisely, the numerical properties of the truncated Pascal's triangle for the extraction of all prime numbers were discovered. Then, arithmetic formulas are presented for the direct extraction of all prime numbers. All of the above is possible after the entire class of numerical tables of truncated triangles has been successfully decoded in the cryptographic system. After these results had been achieved, the general method of establishing the simplest numerical properties of symmetric polynomials of power sums became available. It should be specially noted that only recurrent numerical series are used for the generalization of tables and precise determination of the rules for these tables.