
theorem
  6871 is prime
proof
  now
    6871 = 2*3435 + 1; hence not 2 divides 6871 by NAT_4:9;
    6871 = 3*2290 + 1; hence not 3 divides 6871 by NAT_4:9;
    6871 = 5*1374 + 1; hence not 5 divides 6871 by NAT_4:9;
    6871 = 7*981 + 4; hence not 7 divides 6871 by NAT_4:9;
    6871 = 11*624 + 7; hence not 11 divides 6871 by NAT_4:9;
    6871 = 13*528 + 7; hence not 13 divides 6871 by NAT_4:9;
    6871 = 17*404 + 3; hence not 17 divides 6871 by NAT_4:9;
    6871 = 19*361 + 12; hence not 19 divides 6871 by NAT_4:9;
    6871 = 23*298 + 17; hence not 23 divides 6871 by NAT_4:9;
    6871 = 29*236 + 27; hence not 29 divides 6871 by NAT_4:9;
    6871 = 31*221 + 20; hence not 31 divides 6871 by NAT_4:9;
    6871 = 37*185 + 26; hence not 37 divides 6871 by NAT_4:9;
    6871 = 41*167 + 24; hence not 41 divides 6871 by NAT_4:9;
    6871 = 43*159 + 34; hence not 43 divides 6871 by NAT_4:9;
    6871 = 47*146 + 9; hence not 47 divides 6871 by NAT_4:9;
    6871 = 53*129 + 34; hence not 53 divides 6871 by NAT_4:9;
    6871 = 59*116 + 27; hence not 59 divides 6871 by NAT_4:9;
    6871 = 61*112 + 39; hence not 61 divides 6871 by NAT_4:9;
    6871 = 67*102 + 37; hence not 67 divides 6871 by NAT_4:9;
    6871 = 71*96 + 55; hence not 71 divides 6871 by NAT_4:9;
    6871 = 73*94 + 9; hence not 73 divides 6871 by NAT_4:9;
    6871 = 79*86 + 77; hence not 79 divides 6871 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6871 & n is prime
  holds not n divides 6871 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
