A polynomial is considered prime if it cannot be factored into two non-constant polynomials over a given field. Determining whether a polynomial is prime is a fundamental problem in number theory and has applications in coding theory, cryptography, and other fields. To establish whether a polynomial is prime, various criteria and algorithms have been developed, including Gauss’s lemma, Eisenstein-Lenstra criterion, and Rabin-Rabin-Miller primality test.
