
theorem
  9829 is prime
proof
  now
    9829 = 2*4914 + 1; hence not 2 divides 9829 by NAT_4:9;
    9829 = 3*3276 + 1; hence not 3 divides 9829 by NAT_4:9;
    9829 = 5*1965 + 4; hence not 5 divides 9829 by NAT_4:9;
    9829 = 7*1404 + 1; hence not 7 divides 9829 by NAT_4:9;
    9829 = 11*893 + 6; hence not 11 divides 9829 by NAT_4:9;
    9829 = 13*756 + 1; hence not 13 divides 9829 by NAT_4:9;
    9829 = 17*578 + 3; hence not 17 divides 9829 by NAT_4:9;
    9829 = 19*517 + 6; hence not 19 divides 9829 by NAT_4:9;
    9829 = 23*427 + 8; hence not 23 divides 9829 by NAT_4:9;
    9829 = 29*338 + 27; hence not 29 divides 9829 by NAT_4:9;
    9829 = 31*317 + 2; hence not 31 divides 9829 by NAT_4:9;
    9829 = 37*265 + 24; hence not 37 divides 9829 by NAT_4:9;
    9829 = 41*239 + 30; hence not 41 divides 9829 by NAT_4:9;
    9829 = 43*228 + 25; hence not 43 divides 9829 by NAT_4:9;
    9829 = 47*209 + 6; hence not 47 divides 9829 by NAT_4:9;
    9829 = 53*185 + 24; hence not 53 divides 9829 by NAT_4:9;
    9829 = 59*166 + 35; hence not 59 divides 9829 by NAT_4:9;
    9829 = 61*161 + 8; hence not 61 divides 9829 by NAT_4:9;
    9829 = 67*146 + 47; hence not 67 divides 9829 by NAT_4:9;
    9829 = 71*138 + 31; hence not 71 divides 9829 by NAT_4:9;
    9829 = 73*134 + 47; hence not 73 divides 9829 by NAT_4:9;
    9829 = 79*124 + 33; hence not 79 divides 9829 by NAT_4:9;
    9829 = 83*118 + 35; hence not 83 divides 9829 by NAT_4:9;
    9829 = 89*110 + 39; hence not 89 divides 9829 by NAT_4:9;
    9829 = 97*101 + 32; hence not 97 divides 9829 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9829 & n is prime
  holds not n divides 9829 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
