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.

Abstract

The study aims to examine the relationships between cognitive absorption and E-Learning readiness in the preparatory stage. The study sample consisted of (190) students who were chosen randomly. The Researcher has developed the cognitive absorption and E-Learning readiness scales. A correlational descriptive approach was adopted. The research revealed that there is a positive statistical relationship between cognitive absorption and eLearning readiness.

: Cigarette smoking is a lifestyle behavior that causes significant adverse health effects. Cigarette smoke contains chemicals, many of which are lead to the production of reactive oxygen species (ROS), which can lead to apoptosis and autophagy. To estimate the association of Cigarette smoking with the autophagy and immunity, technology of real time polymerase chain reaction (RTPCR) for gene expression of (LC3A, LC3B, LC3C, myd88) was used. Enzyme-linked immunosorbent assay (ELISA) technique was utilized to measurement the amount of TNF-α protein. The ratios of LC3A/LC3B and LC3B/LC3C were calculated to estimate the autophagy flux. The results indicate the expression of LC3B, LC3C and Myd88 genes in smokers is increased significantly (p

Background. Handball is a team sport that demands quick reflexes and precise motor skills, particularly in shooting. Players' ability to shoot accurately and swiftly while stationary makes upper limb reaction time crucial for success. Objectives. The research objective is to study the relationship between the motor time of the muscles of the arms and the index of accuracy of shooting from constancy in fourth-stage students in handball. Methods. The researchers used the descriptive method because it is one of the methods used in the research on a sample of students of the fourth stage of the college of Physical Education and Sports Sciences, where the sample consisted of 29 male students from the community of origin, 43 students. Results. Th

In this time, most researchers toward about preparation of compounds according to green chemistry. This research describes the preparation of 2-fluoro-5-(substituted benzylideneamino) benzonitrile under reflux and microwave methods. Six azomethine compounds (B1-6) were synthesized by two methods under reflux and assisted microwave with the comparison between the two methods. Reflux method was prepared of azomethine (B1-6) by reaction of 5-amino-2-fluorobenzonitrile with some aldehyde derivatives with (50–100) mL of absolute ethanol and some quantity of GAA and time is limited between (2–5) hours with a yield between (60–70) percent with recrystallization for appropriate solvents. But the microwave-assisted method was synthesized of co