Help:=proc(): print(`GC(n), TestGC(n)`) : end:

#GC(n): the set of prime pairs [p,q] p<q such
#p+q=2*n
GC:=proc(n) local i,S:

S:={}:

for i from 2 to n do

  if isprime(i) and isprime(2*n-i) then
    S:=S union {[i,2*n-i]}:
  fi:
od:
S:
end:

#The number of solutions of p+q=2*N divided by
#N/(log N)^2
TestGC:=proc(N):
evalf(nops(GC(N))/(N/log(N)^2))
:

end: