Looking For P4?

 Before, in the case of Beal Conjecture, $q$, the scaling factor, is a factor of $C^z$, in this case however $q$ need not be a factor of $P1+P2+2$.

Why do lines through two integer markings pass through the center?  They are radial lines of concentric circles.

$q_1$ and $q_2$ are selected when the line through the 1 mark on a lower arc meets the arc $P1+P2+2$ on a integer mark.  These $q_n$ are primes.  $P4$ is then,

$P4=1.q_1$ or

$P4=1.q_2$

Only on the first integer marking on arc $n$ is the factor $P4=1.q_n$, a possible  candidate for $P4$.  All other distances along the lower arcs will not provide a prime factor. $a.p_n$,  $b.p_n$... etc, are not prime.

$P3$ is obtained by $P3=P1+P2+2-P4$.  If it is not a prime number, find the next $p_n$.

Where is the $\cfrac{1}{\pi}$ factor often encountered?  It is hidden in the radius.

Thank you very much, for your Ps and Qs.

Note:  The first integer mark from the vertical is always available no matter what $a$ introduced in the previous post "Missing The Mark Goldbach" dated 02 Jan 2023, is.

The bisector divides $P1+P2-n$ into two odd numbers. $q$ is odd.  Only odd number are considered in turn as factor/primes.