We developed some questions regarding twin prime conjecture by examining the bounded gaps between composite numbers and explained the relations between the formulas regarding composite numbers. Then we proved the twin prime conjecture to answer the new questions raised by proving the expression: \[ \liminf_{n\to\infty} (c_n_+_1 - c_n) \ge 10. \] In addition, we prove many different approaches have been and it has been proved that there must be a twin prime in the range $(p_k_2\cdot p_k_1, p^2_k_1)$, where $p \neq 2$.

"Mem u Zin" holds a paramount status in Kurdish literature, celebrated for its profound exploration of love. Authored by the esteemed Kurdish poet and writer Ahmet Khani in the 17th century, this epic masterpiece represents the pinnacle of literary achievement within the Kurdish cultural milieu. By conducting a concise analysis of "Mem u Zin," our aim was to shed light on the underlying factors that contribute to the perceived separation of Kurdish society from perfection. We provided a comprehensive view of the linguistic obstacles encountered by the Kurds in this exploration.

In this study, I examined the Beals conjecture on the basis of formulas that produce composite numbers, and I developed some other conjectures that, if answered, would be an answer to the Beals conjecture. Apart from this, I have examined the Beals conjecture from another perspective and posed The Germany Problem.