
theorem
  6911 is prime
proof
  now
    6911 = 2*3455 + 1; hence not 2 divides 6911 by NAT_4:9;
    6911 = 3*2303 + 2; hence not 3 divides 6911 by NAT_4:9;
    6911 = 5*1382 + 1; hence not 5 divides 6911 by NAT_4:9;
    6911 = 7*987 + 2; hence not 7 divides 6911 by NAT_4:9;
    6911 = 11*628 + 3; hence not 11 divides 6911 by NAT_4:9;
    6911 = 13*531 + 8; hence not 13 divides 6911 by NAT_4:9;
    6911 = 17*406 + 9; hence not 17 divides 6911 by NAT_4:9;
    6911 = 19*363 + 14; hence not 19 divides 6911 by NAT_4:9;
    6911 = 23*300 + 11; hence not 23 divides 6911 by NAT_4:9;
    6911 = 29*238 + 9; hence not 29 divides 6911 by NAT_4:9;
    6911 = 31*222 + 29; hence not 31 divides 6911 by NAT_4:9;
    6911 = 37*186 + 29; hence not 37 divides 6911 by NAT_4:9;
    6911 = 41*168 + 23; hence not 41 divides 6911 by NAT_4:9;
    6911 = 43*160 + 31; hence not 43 divides 6911 by NAT_4:9;
    6911 = 47*147 + 2; hence not 47 divides 6911 by NAT_4:9;
    6911 = 53*130 + 21; hence not 53 divides 6911 by NAT_4:9;
    6911 = 59*117 + 8; hence not 59 divides 6911 by NAT_4:9;
    6911 = 61*113 + 18; hence not 61 divides 6911 by NAT_4:9;
    6911 = 67*103 + 10; hence not 67 divides 6911 by NAT_4:9;
    6911 = 71*97 + 24; hence not 71 divides 6911 by NAT_4:9;
    6911 = 73*94 + 49; hence not 73 divides 6911 by NAT_4:9;
    6911 = 79*87 + 38; hence not 79 divides 6911 by NAT_4:9;
    6911 = 83*83 + 22; hence not 83 divides 6911 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6911 & n is prime
  holds not n divides 6911 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
