
theorem
  9859 is prime
proof
  now
    9859 = 2*4929 + 1; hence not 2 divides 9859 by NAT_4:9;
    9859 = 3*3286 + 1; hence not 3 divides 9859 by NAT_4:9;
    9859 = 5*1971 + 4; hence not 5 divides 9859 by NAT_4:9;
    9859 = 7*1408 + 3; hence not 7 divides 9859 by NAT_4:9;
    9859 = 11*896 + 3; hence not 11 divides 9859 by NAT_4:9;
    9859 = 13*758 + 5; hence not 13 divides 9859 by NAT_4:9;
    9859 = 17*579 + 16; hence not 17 divides 9859 by NAT_4:9;
    9859 = 19*518 + 17; hence not 19 divides 9859 by NAT_4:9;
    9859 = 23*428 + 15; hence not 23 divides 9859 by NAT_4:9;
    9859 = 29*339 + 28; hence not 29 divides 9859 by NAT_4:9;
    9859 = 31*318 + 1; hence not 31 divides 9859 by NAT_4:9;
    9859 = 37*266 + 17; hence not 37 divides 9859 by NAT_4:9;
    9859 = 41*240 + 19; hence not 41 divides 9859 by NAT_4:9;
    9859 = 43*229 + 12; hence not 43 divides 9859 by NAT_4:9;
    9859 = 47*209 + 36; hence not 47 divides 9859 by NAT_4:9;
    9859 = 53*186 + 1; hence not 53 divides 9859 by NAT_4:9;
    9859 = 59*167 + 6; hence not 59 divides 9859 by NAT_4:9;
    9859 = 61*161 + 38; hence not 61 divides 9859 by NAT_4:9;
    9859 = 67*147 + 10; hence not 67 divides 9859 by NAT_4:9;
    9859 = 71*138 + 61; hence not 71 divides 9859 by NAT_4:9;
    9859 = 73*135 + 4; hence not 73 divides 9859 by NAT_4:9;
    9859 = 79*124 + 63; hence not 79 divides 9859 by NAT_4:9;
    9859 = 83*118 + 65; hence not 83 divides 9859 by NAT_4:9;
    9859 = 89*110 + 69; hence not 89 divides 9859 by NAT_4:9;
    9859 = 97*101 + 62; hence not 97 divides 9859 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9859 & n is prime
  holds not n divides 9859 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
