
theorem
  9851 is prime
proof
  now
    9851 = 2*4925 + 1; hence not 2 divides 9851 by NAT_4:9;
    9851 = 3*3283 + 2; hence not 3 divides 9851 by NAT_4:9;
    9851 = 5*1970 + 1; hence not 5 divides 9851 by NAT_4:9;
    9851 = 7*1407 + 2; hence not 7 divides 9851 by NAT_4:9;
    9851 = 11*895 + 6; hence not 11 divides 9851 by NAT_4:9;
    9851 = 13*757 + 10; hence not 13 divides 9851 by NAT_4:9;
    9851 = 17*579 + 8; hence not 17 divides 9851 by NAT_4:9;
    9851 = 19*518 + 9; hence not 19 divides 9851 by NAT_4:9;
    9851 = 23*428 + 7; hence not 23 divides 9851 by NAT_4:9;
    9851 = 29*339 + 20; hence not 29 divides 9851 by NAT_4:9;
    9851 = 31*317 + 24; hence not 31 divides 9851 by NAT_4:9;
    9851 = 37*266 + 9; hence not 37 divides 9851 by NAT_4:9;
    9851 = 41*240 + 11; hence not 41 divides 9851 by NAT_4:9;
    9851 = 43*229 + 4; hence not 43 divides 9851 by NAT_4:9;
    9851 = 47*209 + 28; hence not 47 divides 9851 by NAT_4:9;
    9851 = 53*185 + 46; hence not 53 divides 9851 by NAT_4:9;
    9851 = 59*166 + 57; hence not 59 divides 9851 by NAT_4:9;
    9851 = 61*161 + 30; hence not 61 divides 9851 by NAT_4:9;
    9851 = 67*147 + 2; hence not 67 divides 9851 by NAT_4:9;
    9851 = 71*138 + 53; hence not 71 divides 9851 by NAT_4:9;
    9851 = 73*134 + 69; hence not 73 divides 9851 by NAT_4:9;
    9851 = 79*124 + 55; hence not 79 divides 9851 by NAT_4:9;
    9851 = 83*118 + 57; hence not 83 divides 9851 by NAT_4:9;
    9851 = 89*110 + 61; hence not 89 divides 9851 by NAT_4:9;
    9851 = 97*101 + 54; hence not 97 divides 9851 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9851 & n is prime
  holds not n divides 9851 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
