
theorem
  1733 is prime
proof
  now
    1733 = 2*866 + 1; hence not 2 divides 1733 by NAT_4:9;
    1733 = 3*577 + 2; hence not 3 divides 1733 by NAT_4:9;
    1733 = 5*346 + 3; hence not 5 divides 1733 by NAT_4:9;
    1733 = 7*247 + 4; hence not 7 divides 1733 by NAT_4:9;
    1733 = 11*157 + 6; hence not 11 divides 1733 by NAT_4:9;
    1733 = 13*133 + 4; hence not 13 divides 1733 by NAT_4:9;
    1733 = 17*101 + 16; hence not 17 divides 1733 by NAT_4:9;
    1733 = 19*91 + 4; hence not 19 divides 1733 by NAT_4:9;
    1733 = 23*75 + 8; hence not 23 divides 1733 by NAT_4:9;
    1733 = 29*59 + 22; hence not 29 divides 1733 by NAT_4:9;
    1733 = 31*55 + 28; hence not 31 divides 1733 by NAT_4:9;
    1733 = 37*46 + 31; hence not 37 divides 1733 by NAT_4:9;
    1733 = 41*42 + 11; hence not 41 divides 1733 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1733 & n is prime
  holds not n divides 1733 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
