
theorem
  6907 is prime
proof
  now
    6907 = 2*3453 + 1; hence not 2 divides 6907 by NAT_4:9;
    6907 = 3*2302 + 1; hence not 3 divides 6907 by NAT_4:9;
    6907 = 5*1381 + 2; hence not 5 divides 6907 by NAT_4:9;
    6907 = 7*986 + 5; hence not 7 divides 6907 by NAT_4:9;
    6907 = 11*627 + 10; hence not 11 divides 6907 by NAT_4:9;
    6907 = 13*531 + 4; hence not 13 divides 6907 by NAT_4:9;
    6907 = 17*406 + 5; hence not 17 divides 6907 by NAT_4:9;
    6907 = 19*363 + 10; hence not 19 divides 6907 by NAT_4:9;
    6907 = 23*300 + 7; hence not 23 divides 6907 by NAT_4:9;
    6907 = 29*238 + 5; hence not 29 divides 6907 by NAT_4:9;
    6907 = 31*222 + 25; hence not 31 divides 6907 by NAT_4:9;
    6907 = 37*186 + 25; hence not 37 divides 6907 by NAT_4:9;
    6907 = 41*168 + 19; hence not 41 divides 6907 by NAT_4:9;
    6907 = 43*160 + 27; hence not 43 divides 6907 by NAT_4:9;
    6907 = 47*146 + 45; hence not 47 divides 6907 by NAT_4:9;
    6907 = 53*130 + 17; hence not 53 divides 6907 by NAT_4:9;
    6907 = 59*117 + 4; hence not 59 divides 6907 by NAT_4:9;
    6907 = 61*113 + 14; hence not 61 divides 6907 by NAT_4:9;
    6907 = 67*103 + 6; hence not 67 divides 6907 by NAT_4:9;
    6907 = 71*97 + 20; hence not 71 divides 6907 by NAT_4:9;
    6907 = 73*94 + 45; hence not 73 divides 6907 by NAT_4:9;
    6907 = 79*87 + 34; hence not 79 divides 6907 by NAT_4:9;
    6907 = 83*83 + 18; hence not 83 divides 6907 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6907 & n is prime
  holds not n divides 6907 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
