Brachylog, 17 bytes

{>I-₂:I{ṗ/₁}ᵐ}ᶠc+

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###Explanation

{            }ᶠ        Find all valid outputs of the predicate in brackets
               c+      Output is the sum of that list after flattening it

 >I                    Input > I
   -₂:I                The list [I-2, I]
       {   }ᵐ          Map:
        ṗ/₁              Must be prime and the output is its inverse

Brachylog, 17 bytes

{>I-₂:I{ṗ/₁}ᵐ}ᶠc+

Try it online!

This is the brand new version of Brachylog, with a shiny code page!

Explanation

{            }ᶠ        Find all valid outputs of the predicate in brackets
               c+      Output is the sum of that list after flattening it

 >I                    Input > I
   -₂:I                The list [I-2, I]
       {   }ᵐ          Map:
        ṗ/₁              Must be prime and the output is its inverse