
theorem
  1109 is prime
proof
  now
    1109 = 2*554 + 1; hence not 2 divides 1109 by NAT_4:9;
    1109 = 3*369 + 2; hence not 3 divides 1109 by NAT_4:9;
    1109 = 5*221 + 4; hence not 5 divides 1109 by NAT_4:9;
    1109 = 7*158 + 3; hence not 7 divides 1109 by NAT_4:9;
    1109 = 11*100 + 9; hence not 11 divides 1109 by NAT_4:9;
    1109 = 13*85 + 4; hence not 13 divides 1109 by NAT_4:9;
    1109 = 17*65 + 4; hence not 17 divides 1109 by NAT_4:9;
    1109 = 19*58 + 7; hence not 19 divides 1109 by NAT_4:9;
    1109 = 23*48 + 5; hence not 23 divides 1109 by NAT_4:9;
    1109 = 29*38 + 7; hence not 29 divides 1109 by NAT_4:9;
    1109 = 31*35 + 24; hence not 31 divides 1109 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1109 & n is prime
  holds not n divides 1109 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
