 Gödel achieved an encoding of a formal language by assigning numbers to symbols, formulas and sequences of formulas, which later became known as “Gödel numbers.” Concretely, Gödel assigned odd numbers to symbols and products of powers of primes (with the number corresponding to  a symbol in the exponent) to sequences of symbols. However, it is possible to  arithmetize the language of CL without placing a strong emphasis on the  existence and the properties of prime numbers. (See for example,  Raymond M. Smullyan’s books: Smullyan (1985) and Smullyan (1994).)  The five symbols get as their Gödel numbers the first five positive  integers. A string is assigned the number in base \(10\) that results from  the concatenation of the corresponding numbers for the symbols.