On twin primes

In this study, some features of prime numbers are examined. In the first part of this work consisting of five chapters, the notation to be used in the study is introduced. In the second part, some properties of prime numbers are examined and Goldbach problems and Riemann and Generalized Riemann Hypothesis are discussed. In addition, the properties of the Riemann-zeta function have been studied. In the third chapter some analytical methods for prime numbers are introduced. In the fourth part, the results of the literature on the existence of prime numbers in short intervals and twin primes including the results of Prof.Dr.Cem Yalçın Yıldırım, who has Cole Prize, are discussed. In the fifth and last chapter, the results obtained on the existence of prime numbers in the interval [4n, 5n], which is a fairly recent result as of the date of presentation of the work. This work is a compilation.