
theorem
  9871 is prime
proof
  now
    9871 = 2*4935 + 1; hence not 2 divides 9871 by NAT_4:9;
    9871 = 3*3290 + 1; hence not 3 divides 9871 by NAT_4:9;
    9871 = 5*1974 + 1; hence not 5 divides 9871 by NAT_4:9;
    9871 = 7*1410 + 1; hence not 7 divides 9871 by NAT_4:9;
    9871 = 11*897 + 4; hence not 11 divides 9871 by NAT_4:9;
    9871 = 13*759 + 4; hence not 13 divides 9871 by NAT_4:9;
    9871 = 17*580 + 11; hence not 17 divides 9871 by NAT_4:9;
    9871 = 19*519 + 10; hence not 19 divides 9871 by NAT_4:9;
    9871 = 23*429 + 4; hence not 23 divides 9871 by NAT_4:9;
    9871 = 29*340 + 11; hence not 29 divides 9871 by NAT_4:9;
    9871 = 31*318 + 13; hence not 31 divides 9871 by NAT_4:9;
    9871 = 37*266 + 29; hence not 37 divides 9871 by NAT_4:9;
    9871 = 41*240 + 31; hence not 41 divides 9871 by NAT_4:9;
    9871 = 43*229 + 24; hence not 43 divides 9871 by NAT_4:9;
    9871 = 47*210 + 1; hence not 47 divides 9871 by NAT_4:9;
    9871 = 53*186 + 13; hence not 53 divides 9871 by NAT_4:9;
    9871 = 59*167 + 18; hence not 59 divides 9871 by NAT_4:9;
    9871 = 61*161 + 50; hence not 61 divides 9871 by NAT_4:9;
    9871 = 67*147 + 22; hence not 67 divides 9871 by NAT_4:9;
    9871 = 71*139 + 2; hence not 71 divides 9871 by NAT_4:9;
    9871 = 73*135 + 16; hence not 73 divides 9871 by NAT_4:9;
    9871 = 79*124 + 75; hence not 79 divides 9871 by NAT_4:9;
    9871 = 83*118 + 77; hence not 83 divides 9871 by NAT_4:9;
    9871 = 89*110 + 81; hence not 89 divides 9871 by NAT_4:9;
    9871 = 97*101 + 74; hence not 97 divides 9871 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9871 & n is prime
  holds not n divides 9871 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
