The following code finds the sole solution of
41  88  47
100 400 100
59  112 53

a=3;

While[a+18<100,

b=a+6;

c=b+6;

d=c+6;

w=a+b;

x=b+c;

y=d+c;

z=a+d;

s=w+x+y+z;

If[PrimeQ[b] && PrimeQ[c] && PrimeQ[d] && IntegerQ[Sqrt[s]],

Print[a," ",w," ",b];

Print[z," ",s," ",x];

Print[d," ",y," ",c];

];

a=NextPrime[a];

];