Abstract
This work studies aspects of RSA public key cryptography and its relationship with number theory, in particular with the properties of prime numbers. The methodology is based on bibliographical research. The study is based on the analysis of bibliographic texts. From analyzing the texts, the strengths of RSA public-key cryptography, also known as RSA asymmetric cryptography, are evident. As strengths, we can mention the greater security against attacks and code breakage by using big keys, even using super modern computers and with ultra-fast data processing and key management for all users of the system. The main disadvantage is the slowness of the encryption process, as it uses generally more complex algorithms and large keys.