I made some adjustments to the coordinates.
Manipulate[ With[{np = NextPrime[xf]}, Plot[{x^2}, {x, -10, xf}, Axes -> {True, True}, Epilog -> { Opacity[0.4], Purple, Line /@ Flatten[ Outer[List, Table[{n, n^2}, {n, 2, np}], Table[{-n, n^2}, {n, 2, np}], 1], 1], Opacity[1], {Black,
Text[#, {#, 0}] & /@ Complement[Range[np], Table[Prime[n], {n, np}]]}, Red, PointSize[0.01], Table[Tooltip[Point@{Prime[n], 0}, Prime[n]], {n, np}], Table[Tooltip[Point@{n, n^2}, n], {n, 2, np}], Table[Tooltip[Point@{-n, n^2}, n], {n, 2, np}] }, ImageSize -> 600 ] ], {{xf, 9, "x"}, 4, 50, Appearance -> "Labeled"} ]
Manipulate[With[{np = NextPrime[xf]}, Plot[{x^2}, {x, -10, xf}, Axes -> {True, True},
Epilog -> { Opacity[0.4], Purple, Line /@ Flatten[ Outer[List, Table[{n, n^2}, {n, 2, np}], Table[{-n, n^2}, {n, 2, np}], 1], 1], Opacity[1], {Black, Text[#, {#, 0}] & /@
Complement[Range[np], Table[Prime[n], {n, np}]]},
Red, PointSize[0.01],
Table[Tooltip[Point@{Prime[n], 0}, Prime[n]], {n, np}],
Table[Tooltip[Point@{n, n^2}, n], {n, 2, np}],
Table[Tooltip[Point@{-n, n^2}, n], {n, 2, np}]
},
ImageSize -> 600
]
],
{{xf, 9, "x"}, 4, 50, Appearance -> "Labeled"}]