
theorem
  1489 is prime
proof
  now
    1489 = 2*744 + 1; hence not 2 divides 1489 by NAT_4:9;
    1489 = 3*496 + 1; hence not 3 divides 1489 by NAT_4:9;
    1489 = 5*297 + 4; hence not 5 divides 1489 by NAT_4:9;
    1489 = 7*212 + 5; hence not 7 divides 1489 by NAT_4:9;
    1489 = 11*135 + 4; hence not 11 divides 1489 by NAT_4:9;
    1489 = 13*114 + 7; hence not 13 divides 1489 by NAT_4:9;
    1489 = 17*87 + 10; hence not 17 divides 1489 by NAT_4:9;
    1489 = 19*78 + 7; hence not 19 divides 1489 by NAT_4:9;
    1489 = 23*64 + 17; hence not 23 divides 1489 by NAT_4:9;
    1489 = 29*51 + 10; hence not 29 divides 1489 by NAT_4:9;
    1489 = 31*48 + 1; hence not 31 divides 1489 by NAT_4:9;
    1489 = 37*40 + 9; hence not 37 divides 1489 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1489 & n is prime
  holds not n divides 1489 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
