
theorem
  4409 is prime
proof
  now
    4409 = 2*2204 + 1; hence not 2 divides 4409 by NAT_4:9;
    4409 = 3*1469 + 2; hence not 3 divides 4409 by NAT_4:9;
    4409 = 5*881 + 4; hence not 5 divides 4409 by NAT_4:9;
    4409 = 7*629 + 6; hence not 7 divides 4409 by NAT_4:9;
    4409 = 11*400 + 9; hence not 11 divides 4409 by NAT_4:9;
    4409 = 13*339 + 2; hence not 13 divides 4409 by NAT_4:9;
    4409 = 17*259 + 6; hence not 17 divides 4409 by NAT_4:9;
    4409 = 19*232 + 1; hence not 19 divides 4409 by NAT_4:9;
    4409 = 23*191 + 16; hence not 23 divides 4409 by NAT_4:9;
    4409 = 29*152 + 1; hence not 29 divides 4409 by NAT_4:9;
    4409 = 31*142 + 7; hence not 31 divides 4409 by NAT_4:9;
    4409 = 37*119 + 6; hence not 37 divides 4409 by NAT_4:9;
    4409 = 41*107 + 22; hence not 41 divides 4409 by NAT_4:9;
    4409 = 43*102 + 23; hence not 43 divides 4409 by NAT_4:9;
    4409 = 47*93 + 38; hence not 47 divides 4409 by NAT_4:9;
    4409 = 53*83 + 10; hence not 53 divides 4409 by NAT_4:9;
    4409 = 59*74 + 43; hence not 59 divides 4409 by NAT_4:9;
    4409 = 61*72 + 17; hence not 61 divides 4409 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4409 & n is prime
  holds not n divides 4409 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
