
theorem
  743 is prime
proof
  now
    743 = 2*371 + 1; hence not 2 divides 743 by NAT_4:9;
    743 = 3*247 + 2; hence not 3 divides 743 by NAT_4:9;
    743 = 5*148 + 3; hence not 5 divides 743 by NAT_4:9;
    743 = 7*106 + 1; hence not 7 divides 743 by NAT_4:9;
    743 = 11*67 + 6; hence not 11 divides 743 by NAT_4:9;
    743 = 13*57 + 2; hence not 13 divides 743 by NAT_4:9;
    743 = 17*43 + 12; hence not 17 divides 743 by NAT_4:9;
    743 = 19*39 + 2; hence not 19 divides 743 by NAT_4:9;
    743 = 23*32 + 7; hence not 23 divides 743 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 743 & n is prime
  holds not n divides 743 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
