In the field of number theory, Fermat numbers have been a topic of significant interest due to their unique properties and implications in various mathematical domains. This study aims to explore the properties and applications of generalized Fermat numbers, extending the classical understanding of Fermat's work. Utilizing a blend of analytical and computational methods, we investigate the divisibility properties and potential applications in cryptography. Our findings reveal new insights into the distribution of factors of generalized Fermat numbers, providing broader implications for prime testing algorithms. The study also highlights potential cryptographic applications, where the security of cryptographic protocols can be enhanced by leveraging the unpredictable nature of these numbers. In conclusion, this research broadens the scope of number theory, offering new perspectives and tools for mathematicians and cryptographers alike. Our results underscore the richness of generalized Fermat numbers, stressing their relevance in both theoretical and practical applications. Further studies are recommended to explore the deeper implications of these findings across other domains of mathematics.