
theorem
  1433 is prime
proof
  now
    1433 = 2*716 + 1; hence not 2 divides 1433 by NAT_4:9;
    1433 = 3*477 + 2; hence not 3 divides 1433 by NAT_4:9;
    1433 = 5*286 + 3; hence not 5 divides 1433 by NAT_4:9;
    1433 = 7*204 + 5; hence not 7 divides 1433 by NAT_4:9;
    1433 = 11*130 + 3; hence not 11 divides 1433 by NAT_4:9;
    1433 = 13*110 + 3; hence not 13 divides 1433 by NAT_4:9;
    1433 = 17*84 + 5; hence not 17 divides 1433 by NAT_4:9;
    1433 = 19*75 + 8; hence not 19 divides 1433 by NAT_4:9;
    1433 = 23*62 + 7; hence not 23 divides 1433 by NAT_4:9;
    1433 = 29*49 + 12; hence not 29 divides 1433 by NAT_4:9;
    1433 = 31*46 + 7; hence not 31 divides 1433 by NAT_4:9;
    1433 = 37*38 + 27; hence not 37 divides 1433 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1433 & n is prime
  holds not n divides 1433 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
