At the first quadrant in the 
-plane, you are asked to construct a line segment with the following specifications:
-plane, you are asked to construct a line segment with the following specifications:- Select a prime point along the x-axis.
- Select an integer point along the y-axis.
- Connect these points to form a line segment.
How many line segments, with the abovementioned specifications, can be constructed that pass through a given point 
?
? For example, in the figure below, it is shown that 2 such lines pass through the point 
, with lines connecting prime points 
and 
to integer points 
and 
, respectively. It can be proven that these are the only line segments, drawn as specified, that pass through .
, with lines connecting prime points and to integer points and , respectively. It can be proven that these are the only line segments, drawn as specified, that pass through .
NOTE: It is possible that no line segments, as specified, pass through a given point.
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