
theorem
  4339 is prime
proof
  now
    4339 = 2*2169 + 1; hence not 2 divides 4339 by NAT_4:9;
    4339 = 3*1446 + 1; hence not 3 divides 4339 by NAT_4:9;
    4339 = 5*867 + 4; hence not 5 divides 4339 by NAT_4:9;
    4339 = 7*619 + 6; hence not 7 divides 4339 by NAT_4:9;
    4339 = 11*394 + 5; hence not 11 divides 4339 by NAT_4:9;
    4339 = 13*333 + 10; hence not 13 divides 4339 by NAT_4:9;
    4339 = 17*255 + 4; hence not 17 divides 4339 by NAT_4:9;
    4339 = 19*228 + 7; hence not 19 divides 4339 by NAT_4:9;
    4339 = 23*188 + 15; hence not 23 divides 4339 by NAT_4:9;
    4339 = 29*149 + 18; hence not 29 divides 4339 by NAT_4:9;
    4339 = 31*139 + 30; hence not 31 divides 4339 by NAT_4:9;
    4339 = 37*117 + 10; hence not 37 divides 4339 by NAT_4:9;
    4339 = 41*105 + 34; hence not 41 divides 4339 by NAT_4:9;
    4339 = 43*100 + 39; hence not 43 divides 4339 by NAT_4:9;
    4339 = 47*92 + 15; hence not 47 divides 4339 by NAT_4:9;
    4339 = 53*81 + 46; hence not 53 divides 4339 by NAT_4:9;
    4339 = 59*73 + 32; hence not 59 divides 4339 by NAT_4:9;
    4339 = 61*71 + 8; hence not 61 divides 4339 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4339 & n is prime
  holds not n divides 4339 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
