python3 - <<'EOF'
from array import array
A=[2,3,4,5,7,9,11,13,16,17,19,23,25,29,31,36,37,41,43,47,49]
N=21
M=1<<N
n=array('B',[0])*M
S=array('i',[0])*M
Q=array('i',[0])*M
for m in range(1,M):
 l=m&-m
 b=l.bit_length()-1
 t=m^l
 n[m]=n[t]+1
 S[m]=S[t]+A[b]
 Q[m]=Q[t]+A[b]*A[b]
P=[(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)]
T={(A[q]-A[p])**2:(p,q) for p,q in P}
H=set()
for m in range(1,M):
 if n[m]>2:
  u=4*(n[m]*Q[m]-S[m]*S[m])
  d=n[m]*n[m]
  if u%d==0 and u//d in T:
   p,q=T[u//d]
   if (m>>p)&1 and (m>>q)&1:
    H.add((p,q))
print(sorted(H))
EOF