How prime numbers are used for cybersecurity?

Can you explain in detail how prime numbers are Leveraged in the realm of cybersecurity? How do they play a crucial role in ensuring the safety and security of digital transactions and communications? I'm particularly interested in understanding the mechanisms behind how they contribute to encryption and how their unique properties make them ideal for this purpose. Could you also elaborate on any real-world applications or examples where prime numbers have been successfully employed to bolster cybersecurity measures?