
theorem
  3433 is prime
proof
  now
    3433 = 2*1716 + 1; hence not 2 divides 3433 by NAT_4:9;
    3433 = 3*1144 + 1; hence not 3 divides 3433 by NAT_4:9;
    3433 = 5*686 + 3; hence not 5 divides 3433 by NAT_4:9;
    3433 = 7*490 + 3; hence not 7 divides 3433 by NAT_4:9;
    3433 = 11*312 + 1; hence not 11 divides 3433 by NAT_4:9;
    3433 = 13*264 + 1; hence not 13 divides 3433 by NAT_4:9;
    3433 = 17*201 + 16; hence not 17 divides 3433 by NAT_4:9;
    3433 = 19*180 + 13; hence not 19 divides 3433 by NAT_4:9;
    3433 = 23*149 + 6; hence not 23 divides 3433 by NAT_4:9;
    3433 = 29*118 + 11; hence not 29 divides 3433 by NAT_4:9;
    3433 = 31*110 + 23; hence not 31 divides 3433 by NAT_4:9;
    3433 = 37*92 + 29; hence not 37 divides 3433 by NAT_4:9;
    3433 = 41*83 + 30; hence not 41 divides 3433 by NAT_4:9;
    3433 = 43*79 + 36; hence not 43 divides 3433 by NAT_4:9;
    3433 = 47*73 + 2; hence not 47 divides 3433 by NAT_4:9;
    3433 = 53*64 + 41; hence not 53 divides 3433 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3433 & n is prime
  holds not n divides 3433 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
