
theorem
  1723 is prime
proof
  now
    1723 = 2*861 + 1; hence not 2 divides 1723 by NAT_4:9;
    1723 = 3*574 + 1; hence not 3 divides 1723 by NAT_4:9;
    1723 = 5*344 + 3; hence not 5 divides 1723 by NAT_4:9;
    1723 = 7*246 + 1; hence not 7 divides 1723 by NAT_4:9;
    1723 = 11*156 + 7; hence not 11 divides 1723 by NAT_4:9;
    1723 = 13*132 + 7; hence not 13 divides 1723 by NAT_4:9;
    1723 = 17*101 + 6; hence not 17 divides 1723 by NAT_4:9;
    1723 = 19*90 + 13; hence not 19 divides 1723 by NAT_4:9;
    1723 = 23*74 + 21; hence not 23 divides 1723 by NAT_4:9;
    1723 = 29*59 + 12; hence not 29 divides 1723 by NAT_4:9;
    1723 = 31*55 + 18; hence not 31 divides 1723 by NAT_4:9;
    1723 = 37*46 + 21; hence not 37 divides 1723 by NAT_4:9;
    1723 = 41*42 + 1; hence not 41 divides 1723 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1723 & n is prime
  holds not n divides 1723 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
