In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

     This research raises the issue of the obligation to ensure safety as the most important obligation of tourism and travel companies in the organized trip contract، which is why a tourist chooses this type of trip، If the tourist aims for entertainment and pleasure، he seeks to be sponsored by the organized company to ensure his safe and healthy return home without any damage ، particularly physical damage  ، Although this commitment is important، it has not received the attention of the Iraqi legislator، so this research is based on an analytical  comparative based on Egyptian and French law as well as English law  ، The legislative experience of these States، as well as the views of the op

Phytoplankton community is a model for of monitoring  aquatic systems and interpreting the environmental change in aquatic systems. The present study aimed to forecast environmental parameters that drive the change of phytoplankton community structure in the lake. The present study was carried out in Baghdad Tourist Island Lake (BTIL) for the period From October 2021 to May 2022. The study included the quality and quantity of phytoplankton, moreover, the highest and lowest value of the physical and chemical parameters were (Water temperature (13-30 °C), Light penetration (94-275cm), electric conductivity (837-1128 µS/cm), salinity (0.5-0.7 ‰), pH (7-8.2), total alkalinity (126-226 mg CaCO3/L), total Hardness (297-395 mg CaCO3/L), Ca

          The organizational culture is considered as an important topic. In this research, this topic was studied in modern paints Industries Company to assess its role in job performance and to show if there is this relationship between them or no. it is, also, attempted to measure this strength of this relationship if any. The 40 cases research sample was chosen. This sample included the chief executive, his assistants, key managers, and their assistants. The questioner consists of two sets of questions : the first set ( concerning the organizational culture) covers six variables (Physical structures , Symbols

The use of data envelopment analysis method helps to improve the performance of organizations in order to exploit their resources efficiently in order to improve the service quality. represented study a problem in need of the Iraqi Middle East Investment Bank to assess the performance of bank branches, according to the service quality provided, Thus, the importance of the study is to contribute using a scientific and systematic method by applying  the data envelopment analysis method in assessing the service quality provided by the bank branches, The study focused on achieving the goal of determining the efficiency of the  services quality provided by the bank branches manner which reflect the extent of utilization of a

Christianity has rites and rituals that they should perform, and are indispensible. They say that these are sacred ordinances by Jesus Christ (PBUH) including the secret of priesthood. The origin of this secret as they claim is Christ. He puts the foundation of priesthood in Christianity. He has chosen twelve disciples and then seventeen whom he ordinated to obtain the honor of spreading the message of Christ among people. He appointed among the priests a divine message which the first fathers from the disciplesthemselves. The disciples are ones who take the secret and deliver it to the ones after them. The disciples took that sacred secret from Christ. Therefore, the secret is used when granting any religious position in the church. That s

Researches military crimes is important and dangerous and it is important in it is violation of the obligation and all forms military order in all, it is dangerous because it affects the interests of the armed forces , military crime is a loophole whose effects are not tangible in normal circumstances however ,in the  crises and wars ,they have serious dimensions , one of the most dangerous and crimes is the crime of fleeing and because the great importance of this crime will be dealt with  in two section will be devoted the first  of the concept of the crime of fleeing and the second will address the legal concept of this crime. 

This study presented more than twenty books that dealt with the subject of (Weights of the Tawshih art), whether their study was independent and dedicated the art of Tawshih as a part of book. Therefore, the review of the sources and references on the art of the Tawshih is not specific for place or time, it was a broad and comprehensive review of all the places where the muwashahat appeared in the east and west, Andalusia was one of the most important areas covered by the study arbic Maghreb and Iraq. The art of tawshih took different forms according to the countries in which they appeared. Muwashahat is a new art that appeared in Andalusia, its main goal was to renew the Khalilian weights and to find the poetic rhythm that fits with the so

In this paper we introduce the idea of the commutator of two fuzzy subsets of a group and study the concept of the commutator of two fuzzy subsets of a group .We introduce and study some of its properties .

Abstract: Various peoples have contributed to building the Islamic civilization through the achievements and creativity of their scholars. In particular, the Kurdish scholars have provided new and great services to the Holy Qur’an that deserves attention. For example, it is no secret that Sheikh Ahmadian, with his interpretation, rendered a great service to the Glorious Book of God. His style is distinguished by modernity, seriousness and objectivity, and represents a lively response to the needs of the Kurdish Muslim people. Due to the importance of Ahmadian’s interpretation of the Qur’an, therefore, I have demonstrated his approach in this research in terms of dealing with his interpretation of the Qur’an with the Qur’an, the