
theorem
  9833 is prime
proof
  now
    9833 = 2*4916 + 1; hence not 2 divides 9833 by NAT_4:9;
    9833 = 3*3277 + 2; hence not 3 divides 9833 by NAT_4:9;
    9833 = 5*1966 + 3; hence not 5 divides 9833 by NAT_4:9;
    9833 = 7*1404 + 5; hence not 7 divides 9833 by NAT_4:9;
    9833 = 11*893 + 10; hence not 11 divides 9833 by NAT_4:9;
    9833 = 13*756 + 5; hence not 13 divides 9833 by NAT_4:9;
    9833 = 17*578 + 7; hence not 17 divides 9833 by NAT_4:9;
    9833 = 19*517 + 10; hence not 19 divides 9833 by NAT_4:9;
    9833 = 23*427 + 12; hence not 23 divides 9833 by NAT_4:9;
    9833 = 29*339 + 2; hence not 29 divides 9833 by NAT_4:9;
    9833 = 31*317 + 6; hence not 31 divides 9833 by NAT_4:9;
    9833 = 37*265 + 28; hence not 37 divides 9833 by NAT_4:9;
    9833 = 41*239 + 34; hence not 41 divides 9833 by NAT_4:9;
    9833 = 43*228 + 29; hence not 43 divides 9833 by NAT_4:9;
    9833 = 47*209 + 10; hence not 47 divides 9833 by NAT_4:9;
    9833 = 53*185 + 28; hence not 53 divides 9833 by NAT_4:9;
    9833 = 59*166 + 39; hence not 59 divides 9833 by NAT_4:9;
    9833 = 61*161 + 12; hence not 61 divides 9833 by NAT_4:9;
    9833 = 67*146 + 51; hence not 67 divides 9833 by NAT_4:9;
    9833 = 71*138 + 35; hence not 71 divides 9833 by NAT_4:9;
    9833 = 73*134 + 51; hence not 73 divides 9833 by NAT_4:9;
    9833 = 79*124 + 37; hence not 79 divides 9833 by NAT_4:9;
    9833 = 83*118 + 39; hence not 83 divides 9833 by NAT_4:9;
    9833 = 89*110 + 43; hence not 89 divides 9833 by NAT_4:9;
    9833 = 97*101 + 36; hence not 97 divides 9833 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9833 & n is prime
  holds not n divides 9833 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
