sum25f.gp

\\ a b c d e
\\ l m n f o
\\ k p g u v
\\ j h x r y
\\ i q w t s

\\ps=[3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 71, 73, 79, 83, 101, 103, 107, 109, 113];
ps=[3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113];

used=Vec(0,25);

{
  for(a=1,25,if(!used[a],
   used[a]=1;
   for(b=1,25,if(!used[b],
    used[b]=1;
    for(c=1,25,if(!used[c],
     used[c]=1;
     for(d=1,25,if(!used[d],
      used[d]=1;
      for(e=1,25,if(!used[e],
       used[e]=1;
       if(isprime(ps[a]+ps[b]+ps[c]+ps[d]+ps[e]),
        for(f=1,25,if(!used[f],
         used[f]=1;
         for(g=1,25,if(!used[g],
          used[g]=1;
          for(h=1,25,if(!used[h],
           used[h]=1;
           for(i=1,25,if(!used[i],
            used[i]=1;
            if(isprime(ps[e]+ps[f]+ps[g]+ps[h]+ps[i]),
             for(j=1,25,if(!used[j],
              used[j]=1;
              for(k=1,25,if(!used[k],
               used[k]=1;
               for(l=1,25,if(!used[l],
                used[l]=1;
                if(isprime(ps[i]+ps[j]+ps[k]+ps[l]+ps[a]),
                 for(m=1,25,if(!used[m],
                  used[m]=1;
                  for(n=1,25,if(!used[n],
                   used[n]=1;
                   for(o=1,25,if(!used[o],
                    used[o]=1;
                    if(isprime(ps[l]+ps[m]+ps[n]+ps[f]+ps[o]),
                     for(p=1,25,if(!used[p],
                      used[p]=1;
                      for(q=1,25,if(!used[q],
                       used[q]=1;
                       if(isprime(ps[b]+ps[m]+ps[p]+ps[h]+ps[q]),
                        for(r=1,25,if(!used[r],
                         used[r]=1;
                         for(s=1,25,if(!used[s],
                          used[s]=1;
                          if(isprime(ps[a]+ps[m]+ps[g]+ps[r]+ps[s]),
                           for(t=1,25,if(!used[t],
                            used[t]=1;
                            for(u=1,25,if(!used[u],
                             used[u]=1;
                             if(isprime(ps[t]+ps[r]+ps[u]+ps[f]+ps[d]),
                              for(v=1,25,if(!used[v],
                               used[v]=1;
                               if(isprime(ps[k]+ps[p]+ps[g]+ps[u]+ps[v]),
                                for(w=1,25,if(!used[w],
                                 used[w]=1;
                                 if(isprime(ps[i]+ps[q]+ps[w]+ps[t]+ps[s]),
                                  for(x=1,25,if(!used[x],
                                   used[x]=1;
                                   if(isprime(ps[w]+ps[x]+ps[g]+ps[n]+ps[c]),
                                    for(y=1,25,if(!used[y],
                                     used[y]=1;
                                     if(isprime(ps[j]+ps[h]+ps[x]+ps[r]+ps[y]),
                                      if(isprime(ps[e]+ps[o]+ps[v]+ps[y]+ps[s]),
                                       print("{[",ps[a],",",ps[b],",",ps[c],",",ps[d],",",ps[e],";");
                                       print(ps[l],",",ps[m],",",ps[n],",",ps[f],",",ps[o],";");
                                       print(ps[k],",",ps[p],",",ps[g],",",ps[u],",",ps[v],";");
                                       print(ps[j],",",ps[h],",",ps[x],",",ps[r],",",ps[y],";");
                                       print(ps[i],",",ps[q],",",ps[w],",",ps[t],",",ps[s],"];}");
                                       quit
                                      );
                                     );
                                     used[y]=0;
                                    ));
                                   );
                                   used[x]=0;
                                  ));
                                 );
                                 used[w]=0;
                                ));
                               );
                               used[v]=0;
                              ));
                             );
                             used[u]=0;
                            ));
                            used[t]=0;
                           ));
                          );
                          used[s]=0;
                         ));
                         used[r]=0;
                        ));
                       );
                       used[q]=0;
                      ));
                      used[p]=0;
                     ));
                    );
                    used[o]=0;
                   ));
                   used[n]=0;
                  ));
                  used[m]=0;
                 ));
                );
                used[l]=0;
               ));
               used[k]=0;
              ));
              used[j]=0;
             ));
            );
            used[i]=0;
           ));
           used[h]=0;
          ));
          used[g]=0;
         ));
         used[f]=0;
        ));
       );
       used[e]=0;
      ));
      used[d]=0;
     ));
     used[c]=0;
    ));
    used[b]=0;
   ));
   used[a]=0;
  ));
}

pi@raspberrypi5:~/PrimeSquares $ gp -q < sum25c.gp
205 primes
[1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277]
M[205,1163]=[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23]

[1159, 1161, 1165, 1167, 1169, 1171, 1173, 1175, 1177, 1179, 1181, 1183, 1185, 1187, 1189, 1191, 1193, 1195, 1197, 1199, 1201, 1203, 1205, 1207, 1209, 1211, 1213, 1215, 1217, 1219, 1221, 1223, 1225, 1227, 1229, 1231, 1233, 1235, 1237, 1239, 1241, 1243, 1245, 1247, 1249, 1251, 1253, 1255, 1257, 1259, 1261, 1263, 1265, 1267, 1269, 1271, 1273, 1275, 1277]
pi@raspberrypi5:~/PrimeSquares $ 

pi@raspberrypi5:~/PrimeSquares $ cat sum25c.gp 
{
  min25=vecsum(primes(26))-2;
  mx=1279-1;
  P=primes([5,mx]);
  print(#P+1," primes");
  M=matrix(1+#P,mx,y,x,Set());
  y=1;M[y,3]=Set([1]);
  foreach(P,p,
    y+=1;
    M[y,p]=Set([1]);
    for(x=1,mx,M[y,x]=setunion(M[y-1,x],M[y,x]));
    for(x=1,mx-p,M[y,x+p]=setunion(Set([e+1|e<-M[y-1,x]]),M[y,x+p]));
  );
  C=[x|x<-primes([min25,mx]),setsearch(M[y,x],25)];
  print(C);
  print("M[205,1163]=",M[y,1163]);
  print("\n",[x|x<-[1..mx],setsearch(M[y,x],25)]);
}
pi@raspberrypi5:~/PrimeSquares $