
theorem
  397 is prime
proof
  now
    397 = 2*198 + 1; hence not 2 divides 397 by NAT_4:9;
    397 = 3*132 + 1; hence not 3 divides 397 by NAT_4:9;
    397 = 5*79 + 2; hence not 5 divides 397 by NAT_4:9;
    397 = 7*56 + 5; hence not 7 divides 397 by NAT_4:9;
    397 = 11*36 + 1; hence not 11 divides 397 by NAT_4:9;
    397 = 13*30 + 7; hence not 13 divides 397 by NAT_4:9;
    397 = 17*23 + 6; hence not 17 divides 397 by NAT_4:9;
    397 = 19*20 + 17; hence not 19 divides 397 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 397 & n is prime
  holds not n divides 397 by XPRIMET1:16;
  hence thesis by NAT_4:14;
