
theorem
  6917 is prime
proof
  now
    6917 = 2*3458 + 1; hence not 2 divides 6917 by NAT_4:9;
    6917 = 3*2305 + 2; hence not 3 divides 6917 by NAT_4:9;
    6917 = 5*1383 + 2; hence not 5 divides 6917 by NAT_4:9;
    6917 = 7*988 + 1; hence not 7 divides 6917 by NAT_4:9;
    6917 = 11*628 + 9; hence not 11 divides 6917 by NAT_4:9;
    6917 = 13*532 + 1; hence not 13 divides 6917 by NAT_4:9;
    6917 = 17*406 + 15; hence not 17 divides 6917 by NAT_4:9;
    6917 = 19*364 + 1; hence not 19 divides 6917 by NAT_4:9;
    6917 = 23*300 + 17; hence not 23 divides 6917 by NAT_4:9;
    6917 = 29*238 + 15; hence not 29 divides 6917 by NAT_4:9;
    6917 = 31*223 + 4; hence not 31 divides 6917 by NAT_4:9;
    6917 = 37*186 + 35; hence not 37 divides 6917 by NAT_4:9;
    6917 = 41*168 + 29; hence not 41 divides 6917 by NAT_4:9;
    6917 = 43*160 + 37; hence not 43 divides 6917 by NAT_4:9;
    6917 = 47*147 + 8; hence not 47 divides 6917 by NAT_4:9;
    6917 = 53*130 + 27; hence not 53 divides 6917 by NAT_4:9;
    6917 = 59*117 + 14; hence not 59 divides 6917 by NAT_4:9;
    6917 = 61*113 + 24; hence not 61 divides 6917 by NAT_4:9;
    6917 = 67*103 + 16; hence not 67 divides 6917 by NAT_4:9;
    6917 = 71*97 + 30; hence not 71 divides 6917 by NAT_4:9;
    6917 = 73*94 + 55; hence not 73 divides 6917 by NAT_4:9;
    6917 = 79*87 + 44; hence not 79 divides 6917 by NAT_4:9;
    6917 = 83*83 + 28; hence not 83 divides 6917 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6917 & n is prime
  holds not n divides 6917 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
