Pulling Hair Off Goldbach

From the previous post "More Prime Spiral Goldbach" dated 24 Dec 2022,

 $n_{gi+1}+n_{oi+1}=n_{g}+n_{o}+i+1$            $i$ is odd, 1, 3, 5...

predicts the next pair $n_{gi+1}$ and $n_{oi+1}$ from an odd position $i$ odd.

$n_{gi+1}+n_{oi+1}=(2n+(i+1)-2)-n_{g}-n_{o}$  $i$ is even, 2, 4, 6

predicts the next pair $n_{gi+1}$ and $n_{oi+1}$ from a even position $i$ even.

Since $n_{gi+1}$ and $n_{oi+1}$ is not guaranteed to ensure,

$2(n+i+1)-2n_{oi+1}+1=p_{i+1}$ and $2(n+i+1)-2n_{gi+1}+1=q_{i+1}$

where both $p_{i+1}$ and $q_{i+1}$ are prime and,

$p_{i+1} +q_{i+1}=2(n+i+1)$

Goldbach's Conjecture not proven here.

But take any pair of primes, $p$ and $q$ and calculate,

$n=\cfrac{p+q}{2}$

$n_o=\cfrac{2n-p+1}{2}$ and

$n_p=\cfrac{2n-q+1}{2}$ 

starting with the odd position prediction find candidates for $n_{g1}$ and $n_{o1}$ under the constrain,

$p_{1} +q_{1}=2(n+1)$

then use the even position prediction to find candidates for $n_{g2}$ and $n_{o2}$ under the constrain,

$p_{2} +q_{2}=2(n+2)$

repeat till no possible candidates for $n_{gi}$ and $n_{oi}$ can be found.  The series ends.

Does Goldbach has long hairs?  Spirally long hairs?