area of n-gon of prime points

Question

Using prime points (2,3), (5,7) (11,13)....to a last prime point to form an irregular n-gon by connecting each consecutive point with a line and connecting the first point to the last point with NO previous line being intersected by this longest line, do you think there is some n-gon of maximum area? After this, all increasing last points will have a connecting line from (2,3) to this last point that will always intersect some previous line. As an example. I want to go from (2,3) to (59,61) without having this line intersect any of the previous lines connecting successive prime points. It can be done to give an n-gon with an area of 127. Clarity for this question would result if you drew a graph for the first 20 prime points to observe what the curve is doing. A variation of this question arises when prime points are redefined as (2,3), (3,5), (5,7)...and one connects (2,3) to a final point of this form to give an n-gon having no intersections of the connecting line with any of the lines connecting the previous points. Example of this is going from (2,3) to (41,43) to give an area of 200; from (2,3) to (71,73) the area of 381. In either case of how prime points are defined, do you think there is a maximum n-gon for each in which the connecting line does not intersect any previous connecting lines between successive points?