Monday, January 2, 2023

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.