Positive integer factorization has raised concern particularly in the security of communication technology, based on the fact that positive integers can be employed in the safety of information in cryptography. This study, revealed an infinite square table which is instrumental in the analysis of all positive integer regarding their prime factors. Formula or instructions came up following the orderly arrangement of the positive integers. Moreover, a formula to test primality of a number become obvious in this study. In this regard, positive integers particularly can all potentially be factorized. While it is a solution in mathematics, this can pose threat in the safety communication technology. Nevertheless, this is on one side a solution in cryptography for the fact that a new page is opened to advance the safety of information. Had it been the case that this study did not reveal this fact, the information technology could be at risk. Therefore, the study is about knowledge to communication technology stakeholders to consider safety modification in information systems.

The National Examination Council of Tanzania serves to sort out proper career progress of secondary school students. This study demonstrates future implication to Science, Technology, Engineering, and Mathematics (STEM) careers of candidates who sat for the Certificate of Secondary School Education (CSEE) in Mbeya city. Results collected from 58 schools, of which 32 were private schools. Number of candidates were roughly 8000 of which more than a quarter were from private schools. This study revealed that less than 40% of graduates were potential STEM careers out of which less than one third were girls. Interestingly, performance was free of gender disparity in private schools. On the other hand, boys outperformed girls in STEM subjects from public schools. Overall STEM performance showed that the smallest number of students about 13% passed physics compared to other STEM subjects in public school with number of boys being twice that of girls. Moreover, the study revealed that physics along with mathematics are the determinants of STEM career prospects. Therefore, at least 13% candidates were in the position to further studies in STEM careers from public schools.