
theorem
  1439 is prime
proof
  now
    1439 = 2*719 + 1; hence not 2 divides 1439 by NAT_4:9;
    1439 = 3*479 + 2; hence not 3 divides 1439 by NAT_4:9;
    1439 = 5*287 + 4; hence not 5 divides 1439 by NAT_4:9;
    1439 = 7*205 + 4; hence not 7 divides 1439 by NAT_4:9;
    1439 = 11*130 + 9; hence not 11 divides 1439 by NAT_4:9;
    1439 = 13*110 + 9; hence not 13 divides 1439 by NAT_4:9;
    1439 = 17*84 + 11; hence not 17 divides 1439 by NAT_4:9;
    1439 = 19*75 + 14; hence not 19 divides 1439 by NAT_4:9;
    1439 = 23*62 + 13; hence not 23 divides 1439 by NAT_4:9;
    1439 = 29*49 + 18; hence not 29 divides 1439 by NAT_4:9;
    1439 = 31*46 + 13; hence not 31 divides 1439 by NAT_4:9;
    1439 = 37*38 + 33; hence not 37 divides 1439 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1439 & n is prime
  holds not n divides 1439 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
