If the Goldbach conjecture is true, such a scheme would be all zeros except in up two places, as long as the integer you want to encode is even. Even if the co

If the Goldbach conjecture is true, such a scheme would be all zeros except in up two places, as long as the integer you want to encode is even. Even if the conjecture is true, the code must be ternary: to encode 6 you need to indicate 3 twice, as 6 = 3 + 3. However, very many even integers are the total of more than one pair of primes. So, the encoding of a number using this scheme is not unique. In contrast, because of the property F_n = F_{n-1} + F_{n-2} you never need more any Fibonacci number more than once in the code, so the code is binary (and the encoding unique).