
theorem
  9839 is prime
proof
  now
    9839 = 2*4919 + 1; hence not 2 divides 9839 by NAT_4:9;
    9839 = 3*3279 + 2; hence not 3 divides 9839 by NAT_4:9;
    9839 = 5*1967 + 4; hence not 5 divides 9839 by NAT_4:9;
    9839 = 7*1405 + 4; hence not 7 divides 9839 by NAT_4:9;
    9839 = 11*894 + 5; hence not 11 divides 9839 by NAT_4:9;
    9839 = 13*756 + 11; hence not 13 divides 9839 by NAT_4:9;
    9839 = 17*578 + 13; hence not 17 divides 9839 by NAT_4:9;
    9839 = 19*517 + 16; hence not 19 divides 9839 by NAT_4:9;
    9839 = 23*427 + 18; hence not 23 divides 9839 by NAT_4:9;
    9839 = 29*339 + 8; hence not 29 divides 9839 by NAT_4:9;
    9839 = 31*317 + 12; hence not 31 divides 9839 by NAT_4:9;
    9839 = 37*265 + 34; hence not 37 divides 9839 by NAT_4:9;
    9839 = 41*239 + 40; hence not 41 divides 9839 by NAT_4:9;
    9839 = 43*228 + 35; hence not 43 divides 9839 by NAT_4:9;
    9839 = 47*209 + 16; hence not 47 divides 9839 by NAT_4:9;
    9839 = 53*185 + 34; hence not 53 divides 9839 by NAT_4:9;
    9839 = 59*166 + 45; hence not 59 divides 9839 by NAT_4:9;
    9839 = 61*161 + 18; hence not 61 divides 9839 by NAT_4:9;
    9839 = 67*146 + 57; hence not 67 divides 9839 by NAT_4:9;
    9839 = 71*138 + 41; hence not 71 divides 9839 by NAT_4:9;
    9839 = 73*134 + 57; hence not 73 divides 9839 by NAT_4:9;
    9839 = 79*124 + 43; hence not 79 divides 9839 by NAT_4:9;
    9839 = 83*118 + 45; hence not 83 divides 9839 by NAT_4:9;
    9839 = 89*110 + 49; hence not 89 divides 9839 by NAT_4:9;
    9839 = 97*101 + 42; hence not 97 divides 9839 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9839 & n is prime
  holds not n divides 9839 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
