Gödel numbering assigns a unique number to each formula.
To contruct this we first assign a natural number to each symbol.
This gives us a sequence:
\(\{x_1, x_2, x_3,...,x_n\}\)
We can assign a unique number to this by using the first \(n\) prime numbers.
\(2^{x_1}3^{x_2}5^{x_3}...\)
This number can then be prime factored to recover the sequence, and therefore the formula.