
theorem
  947 is prime
proof
  now
    947 = 2*473 + 1; hence not 2 divides 947 by NAT_4:9;
    947 = 3*315 + 2; hence not 3 divides 947 by NAT_4:9;
    947 = 5*189 + 2; hence not 5 divides 947 by NAT_4:9;
    947 = 7*135 + 2; hence not 7 divides 947 by NAT_4:9;
    947 = 11*86 + 1; hence not 11 divides 947 by NAT_4:9;
    947 = 13*72 + 11; hence not 13 divides 947 by NAT_4:9;
    947 = 17*55 + 12; hence not 17 divides 947 by NAT_4:9;
    947 = 19*49 + 16; hence not 19 divides 947 by NAT_4:9;
    947 = 23*41 + 4; hence not 23 divides 947 by NAT_4:9;
    947 = 29*32 + 19; hence not 29 divides 947 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 947 & n is prime
  holds not n divides 947 by XPRIMET1:20;
  hence thesis by NAT_4:14;
