Prime-cubes can be good too!

There are three good numbers between $1$ and $10^9$ , namely $1302571 \qquad 77767777 \qquad 945134639$ Observe that $\begin{array}{rcl} 1302571^3 & = & 2210060766154315411 \\ 1302571 & = & 221006 + (0)766154 + 315411 \\ 77767777^3 & = & 470326072320873707526433 \\ 77767777 & = & 47032607 + 23208737 + (0)7526433 \\ 945134639^3 & = & 844269384373282700092959119 \\ 945134639 & = & 8442693 + 843732827 + (000)92959119 \end{array}$ There are no others. I listed the $50847534$ primes between $1$ and $10^9$ (an export from Mathematica), and tested these numbers for goodness, using the Delphi code:

function TForm1.HalfGood(u: string): Boolean; 
var
a,b,aa,bb: Integer;
bc: String;
p,q,r,s: Int64;
begin
 bc := BigCube(StrToInt(u));
 s := StrToInt(u);  
 Result := False;
 for a := 1 to Length(u) do
   for b := a+1 to Length(bc) do
     begin
       aa := a+1;
       while ((aa <= b) and (bc[aa] = '0')) do Inc(aa);
       if b + 1 - aa > Length(u) then continue;
       bb := b+1;
       while ((bb <= Length(bc)) and (bc[bb] = '0')) do Inc(bb);
       if Length(bc) + 1 - bb > Length(u) then continue;
       p := StrToInt(Copy(bc,1,a));
       if aa > b then
         q := 0
       else
         q := StrToInt(Copy(bc,aa,b+1-aa));
       if bb > Length(bc) then
         r := 0
       else
         r := StrToInt(Copy(bc,bb,Length(bc)));
       if p+q+r = s then
        begin
          Result := True;
          exit;
        end;
     end;
 end;

where BigCube is a routine that provides the decimal expansion of the cube of a number less than $10^{10}$ as a string.

Since, modulo $10^{10}$ , we have $\begin{array}{rcl} 1302571^{1302571} & \equiv & 7128273571 \\ 77767777^{77767777} & \equiv & 1393177697 \\ 945134639^{945134639} & \equiv & 7264657359 \end{array}$ the answer is $5786109027$ .