Does sha256 use prime numbers?

I'm curious to understand the cryptographic foundations of SHA-256. Can you clarify whether SHA-256 employs prime numbers in its hashing algorithm? If so, how are these prime numbers utilized, and what role do they play in ensuring the security and integrity of SHA-256's output? Additionally, are there any alternative cryptographic mechanisms or mathematical principles that SHA-256 relies on besides prime numbers, and if so, how do they contribute to its overall security?