A novel method for design and implementation of a covert channel using a prime-based mimic function is presented. The main idea is to map the production rules of a context-free grammar onto a set of prime numbers, and encode messages using primes as factors so that the generated data fits the statistical properties of a given language. The method's performance is assessed through different metrics such as language perplexities, secret-to-cover ratio, and transmission bit-rates. A set of experiments shows that prime-based mimic functions provide an efficient method for implementing a covert channel with a competitive secret-to-cover ratio and low perplexities.