The Rivest–Shamir–Adleman (RSA) and the Diffie-Hellman (DH) key exchange are famous methods for encryption. These methods  depended on selecting the primes p and q in order  to be secure enough . This paper shows that the named methods used the primes which are found by some arithmetical function .In the other sense, no need to think about getting primes p and q and how they are secure enough, since the arithmetical function enable to build the primes in such complicated way to be secure. Moreover, this article   gives  new construction  of the  RSA  algorithm and DH key  exchange using the

primes p,qfrom areal number x.

  The search is an application for one of the problems of mathematics in the computer; as providing construction and design of a major program to calculate the inverse permutations of the symmetric group Sn , where 1 ≤ n ≤ 13; using some of the methods used in the Number Theory by computer . Also the research includes design flow chart for the main program and design flow chart for the program inverse permutations and we give some illustrative examples for different symmetric groups and their inverse permutations.

The estimation of the parameters of linear regression is based on the usual Least Square method, as this method is based on the estimation of several basic assumptions. Therefore, the accuracy of estimating the parameters of the model depends on the validity of these hypotheses. The most successful technique was the robust estimation method which is minimizing maximum likelihood estimator (MM-estimator) that proved its efficiency in this purpose. However, the use of the model becomes unrealistic and one of these assumptions is the uniformity of the variance and the normal distribution of the error. These assumptions are not achievable in the case of studying a specific problem that may include complex data of more than one model. To

In The Name of Allah Most Gracious Most Merciful

Scholars, past and present, have paid attention to the books of Fasting and Hajj, and they have compiled literature on that, and they have written treatises and researches. The best days, and as for the pilgrimage, it is one of the great pillars of Islam, which God Almighty has distinguished by making its rituals in the best of places, which is the Sacred House of God.