
theorem
  1447 is prime
proof
  now
    1447 = 2*723 + 1; hence not 2 divides 1447 by NAT_4:9;
    1447 = 3*482 + 1; hence not 3 divides 1447 by NAT_4:9;
    1447 = 5*289 + 2; hence not 5 divides 1447 by NAT_4:9;
    1447 = 7*206 + 5; hence not 7 divides 1447 by NAT_4:9;
    1447 = 11*131 + 6; hence not 11 divides 1447 by NAT_4:9;
    1447 = 13*111 + 4; hence not 13 divides 1447 by NAT_4:9;
    1447 = 17*85 + 2; hence not 17 divides 1447 by NAT_4:9;
    1447 = 19*76 + 3; hence not 19 divides 1447 by NAT_4:9;
    1447 = 23*62 + 21; hence not 23 divides 1447 by NAT_4:9;
    1447 = 29*49 + 26; hence not 29 divides 1447 by NAT_4:9;
    1447 = 31*46 + 21; hence not 31 divides 1447 by NAT_4:9;
    1447 = 37*39 + 4; hence not 37 divides 1447 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1447 & n is prime
  holds not n divides 1447 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
