
theorem
  9857 is prime
proof
  now
    9857 = 2*4928 + 1; hence not 2 divides 9857 by NAT_4:9;
    9857 = 3*3285 + 2; hence not 3 divides 9857 by NAT_4:9;
    9857 = 5*1971 + 2; hence not 5 divides 9857 by NAT_4:9;
    9857 = 7*1408 + 1; hence not 7 divides 9857 by NAT_4:9;
    9857 = 11*896 + 1; hence not 11 divides 9857 by NAT_4:9;
    9857 = 13*758 + 3; hence not 13 divides 9857 by NAT_4:9;
    9857 = 17*579 + 14; hence not 17 divides 9857 by NAT_4:9;
    9857 = 19*518 + 15; hence not 19 divides 9857 by NAT_4:9;
    9857 = 23*428 + 13; hence not 23 divides 9857 by NAT_4:9;
    9857 = 29*339 + 26; hence not 29 divides 9857 by NAT_4:9;
    9857 = 31*317 + 30; hence not 31 divides 9857 by NAT_4:9;
    9857 = 37*266 + 15; hence not 37 divides 9857 by NAT_4:9;
    9857 = 41*240 + 17; hence not 41 divides 9857 by NAT_4:9;
    9857 = 43*229 + 10; hence not 43 divides 9857 by NAT_4:9;
    9857 = 47*209 + 34; hence not 47 divides 9857 by NAT_4:9;
    9857 = 53*185 + 52; hence not 53 divides 9857 by NAT_4:9;
    9857 = 59*167 + 4; hence not 59 divides 9857 by NAT_4:9;
    9857 = 61*161 + 36; hence not 61 divides 9857 by NAT_4:9;
    9857 = 67*147 + 8; hence not 67 divides 9857 by NAT_4:9;
    9857 = 71*138 + 59; hence not 71 divides 9857 by NAT_4:9;
    9857 = 73*135 + 2; hence not 73 divides 9857 by NAT_4:9;
    9857 = 79*124 + 61; hence not 79 divides 9857 by NAT_4:9;
    9857 = 83*118 + 63; hence not 83 divides 9857 by NAT_4:9;
    9857 = 89*110 + 67; hence not 89 divides 9857 by NAT_4:9;
    9857 = 97*101 + 60; hence not 97 divides 9857 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9857 & n is prime
  holds not n divides 9857 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
