Prime Necklace and Goldbach conjecture

A necklace with beads numbered from 1 to 31. The beads having prime numbers are spherical, the beads having composite numbers are ellipsoidal (and 1 is on a smaller sphere).
It can be used to illustrate the Goldbach conjecture: any even number 2n larger than 2 is the sum of two primes p1 and p2: 2n=p1+p2.
If you divide all by 2 you obtain that for any number n, n=(p1+p2)/2 that is: whatever number n is it is exactly at the middle distance of two primes.
To illustrate that, take the necklace by the bead number n (whatever its shape) and let the two ends hang freely: you will always find two spherical beads side by side.
Actually this works only from number 4 to number 27 and for number 30, because:
- for small numbers, 2n must at least equal to 8 for the two prime to be distinct, so it does not work for 2 and 3 but actually the property is interesting mostly for composite numbers since a prime is always the average of itself and itself (2 and 3 are prime, 1 is not consider as prime neither composite)
- for large numbers the problem is that the necklace is not infinite, so some primes will always be missing to complete the equality (here 28, 29 or 31 would need larger primes).