
theorem
  673 is prime
proof
  now
    673 = 2*336 + 1; hence not 2 divides 673 by NAT_4:9;
    673 = 3*224 + 1; hence not 3 divides 673 by NAT_4:9;
    673 = 5*134 + 3; hence not 5 divides 673 by NAT_4:9;
    673 = 7*96 + 1; hence not 7 divides 673 by NAT_4:9;
    673 = 11*61 + 2; hence not 11 divides 673 by NAT_4:9;
    673 = 13*51 + 10; hence not 13 divides 673 by NAT_4:9;
    673 = 17*39 + 10; hence not 17 divides 673 by NAT_4:9;
    673 = 19*35 + 8; hence not 19 divides 673 by NAT_4:9;
    673 = 23*29 + 6; hence not 23 divides 673 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 673 & n is prime
  holds not n divides 673 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
