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Find the sum of all integers "n" such that this expression is prime and \({n}^{2}<{ 10 }^{ { 10 }^{ 100 } }\):-

\(\frac { 6\left\lfloor \pi { n }^{ 12 } \right\rfloor +4\left\lceil \pi { n }^{ 8 } \right\rceil +2\left\lfloor \pi { n }^{ 16 } \right\rfloor +3 }{ 7\left\lceil \pi { n }^{ 8 } \right\rceil +1 } \)

Let the sum be A. Find the sum of digits of A

If there are no solutions to "n", write 0.5. If the sum is infinite/interdeterminant, write 1.5 If the sum of the digits of A is greater than a googol (\({ 10 }^{ 100 }\)), write 2.5.

\( \text{ This is an entry in the troll king contest} \)

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