
theorem
  9791 is prime
proof
  now
    9791 = 2*4895 + 1; hence not 2 divides 9791 by NAT_4:9;
    9791 = 3*3263 + 2; hence not 3 divides 9791 by NAT_4:9;
    9791 = 5*1958 + 1; hence not 5 divides 9791 by NAT_4:9;
    9791 = 7*1398 + 5; hence not 7 divides 9791 by NAT_4:9;
    9791 = 11*890 + 1; hence not 11 divides 9791 by NAT_4:9;
    9791 = 13*753 + 2; hence not 13 divides 9791 by NAT_4:9;
    9791 = 17*575 + 16; hence not 17 divides 9791 by NAT_4:9;
    9791 = 19*515 + 6; hence not 19 divides 9791 by NAT_4:9;
    9791 = 23*425 + 16; hence not 23 divides 9791 by NAT_4:9;
    9791 = 29*337 + 18; hence not 29 divides 9791 by NAT_4:9;
    9791 = 31*315 + 26; hence not 31 divides 9791 by NAT_4:9;
    9791 = 37*264 + 23; hence not 37 divides 9791 by NAT_4:9;
    9791 = 41*238 + 33; hence not 41 divides 9791 by NAT_4:9;
    9791 = 43*227 + 30; hence not 43 divides 9791 by NAT_4:9;
    9791 = 47*208 + 15; hence not 47 divides 9791 by NAT_4:9;
    9791 = 53*184 + 39; hence not 53 divides 9791 by NAT_4:9;
    9791 = 59*165 + 56; hence not 59 divides 9791 by NAT_4:9;
    9791 = 61*160 + 31; hence not 61 divides 9791 by NAT_4:9;
    9791 = 67*146 + 9; hence not 67 divides 9791 by NAT_4:9;
    9791 = 71*137 + 64; hence not 71 divides 9791 by NAT_4:9;
    9791 = 73*134 + 9; hence not 73 divides 9791 by NAT_4:9;
    9791 = 79*123 + 74; hence not 79 divides 9791 by NAT_4:9;
    9791 = 83*117 + 80; hence not 83 divides 9791 by NAT_4:9;
    9791 = 89*110 + 1; hence not 89 divides 9791 by NAT_4:9;
    9791 = 97*100 + 91; hence not 97 divides 9791 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9791 & n is prime
  holds not n divides 9791 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
