Consider the following integral:


And consider functions :



I want to compare them with each other ( at least numerically for large interval of value )

If graph for very large intervals (upto atleast $10^4$) possible please add ( please add all the graph in one axis system so I can compare them ).

(Due to wild oscillations of $S(q)$; I can't deal with it )( Mathematica doesn't seem to help with large values ).

(Does numerics suggests $S(q) \sim R(q)$ or $T(q)$? ).

See ; Related : Towards a new proof of infinitude of primes ( with possible unified application to other primes of special forms whose Infinitude is unknown):

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    $\begingroup$ If I understand correctly, you want a graph of those three function with $2\le q\le10^4$? $\endgroup$ – Jan Eerland May 7 at 13:55
  • $\begingroup$ @Jan yes! That's what I want $\endgroup$ – Bambi May 7 at 13:57
  • $\begingroup$ Why a close vote !? $\endgroup$ – Bambi May 7 at 13:58
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    $\begingroup$ I already mentioned the link where all the details are mentioned , why to repeat again ? $\endgroup$ – Bambi May 7 at 14:06

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