
theorem
  389 is prime
proof
  now
    389 = 2*194 + 1; hence not 2 divides 389 by NAT_4:9;
    389 = 3*129 + 2; hence not 3 divides 389 by NAT_4:9;
    389 = 5*77 + 4; hence not 5 divides 389 by NAT_4:9;
    389 = 7*55 + 4; hence not 7 divides 389 by NAT_4:9;
    389 = 11*35 + 4; hence not 11 divides 389 by NAT_4:9;
    389 = 13*29 + 12; hence not 13 divides 389 by NAT_4:9;
    389 = 17*22 + 15; hence not 17 divides 389 by NAT_4:9;
    389 = 19*20 + 9; hence not 19 divides 389 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 389 & n is prime
  holds not n divides 389 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
