forprime(j=1,1000,\
   if(j%3==2,\
    exception=0:\
    for(x=1,j-1,\
     for(y=1,x,\
      if( ((x+y)%j!=0)&&\
         ( (x^(j)+y^(j)-(x+y)^(j))%((j)^2)==0),\
       exception=1,\
      )\
     )\
    ):\
    if(exception,\
     print1(j," "),\
    ),\
   )\
  )