
theorem
  9811 is prime
proof
  now
    9811 = 2*4905 + 1; hence not 2 divides 9811 by NAT_4:9;
    9811 = 3*3270 + 1; hence not 3 divides 9811 by NAT_4:9;
    9811 = 5*1962 + 1; hence not 5 divides 9811 by NAT_4:9;
    9811 = 7*1401 + 4; hence not 7 divides 9811 by NAT_4:9;
    9811 = 11*891 + 10; hence not 11 divides 9811 by NAT_4:9;
    9811 = 13*754 + 9; hence not 13 divides 9811 by NAT_4:9;
    9811 = 17*577 + 2; hence not 17 divides 9811 by NAT_4:9;
    9811 = 19*516 + 7; hence not 19 divides 9811 by NAT_4:9;
    9811 = 23*426 + 13; hence not 23 divides 9811 by NAT_4:9;
    9811 = 29*338 + 9; hence not 29 divides 9811 by NAT_4:9;
    9811 = 31*316 + 15; hence not 31 divides 9811 by NAT_4:9;
    9811 = 37*265 + 6; hence not 37 divides 9811 by NAT_4:9;
    9811 = 41*239 + 12; hence not 41 divides 9811 by NAT_4:9;
    9811 = 43*228 + 7; hence not 43 divides 9811 by NAT_4:9;
    9811 = 47*208 + 35; hence not 47 divides 9811 by NAT_4:9;
    9811 = 53*185 + 6; hence not 53 divides 9811 by NAT_4:9;
    9811 = 59*166 + 17; hence not 59 divides 9811 by NAT_4:9;
    9811 = 61*160 + 51; hence not 61 divides 9811 by NAT_4:9;
    9811 = 67*146 + 29; hence not 67 divides 9811 by NAT_4:9;
    9811 = 71*138 + 13; hence not 71 divides 9811 by NAT_4:9;
    9811 = 73*134 + 29; hence not 73 divides 9811 by NAT_4:9;
    9811 = 79*124 + 15; hence not 79 divides 9811 by NAT_4:9;
    9811 = 83*118 + 17; hence not 83 divides 9811 by NAT_4:9;
    9811 = 89*110 + 21; hence not 89 divides 9811 by NAT_4:9;
    9811 = 97*101 + 14; hence not 97 divides 9811 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9811 & n is prime
  holds not n divides 9811 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
