
theorem
  6679 is prime
proof
  now
    6679 = 2*3339 + 1; hence not 2 divides 6679 by NAT_4:9;
    6679 = 3*2226 + 1; hence not 3 divides 6679 by NAT_4:9;
    6679 = 5*1335 + 4; hence not 5 divides 6679 by NAT_4:9;
    6679 = 7*954 + 1; hence not 7 divides 6679 by NAT_4:9;
    6679 = 11*607 + 2; hence not 11 divides 6679 by NAT_4:9;
    6679 = 13*513 + 10; hence not 13 divides 6679 by NAT_4:9;
    6679 = 17*392 + 15; hence not 17 divides 6679 by NAT_4:9;
    6679 = 19*351 + 10; hence not 19 divides 6679 by NAT_4:9;
    6679 = 23*290 + 9; hence not 23 divides 6679 by NAT_4:9;
    6679 = 29*230 + 9; hence not 29 divides 6679 by NAT_4:9;
    6679 = 31*215 + 14; hence not 31 divides 6679 by NAT_4:9;
    6679 = 37*180 + 19; hence not 37 divides 6679 by NAT_4:9;
    6679 = 41*162 + 37; hence not 41 divides 6679 by NAT_4:9;
    6679 = 43*155 + 14; hence not 43 divides 6679 by NAT_4:9;
    6679 = 47*142 + 5; hence not 47 divides 6679 by NAT_4:9;
    6679 = 53*126 + 1; hence not 53 divides 6679 by NAT_4:9;
    6679 = 59*113 + 12; hence not 59 divides 6679 by NAT_4:9;
    6679 = 61*109 + 30; hence not 61 divides 6679 by NAT_4:9;
    6679 = 67*99 + 46; hence not 67 divides 6679 by NAT_4:9;
    6679 = 71*94 + 5; hence not 71 divides 6679 by NAT_4:9;
    6679 = 73*91 + 36; hence not 73 divides 6679 by NAT_4:9;
    6679 = 79*84 + 43; hence not 79 divides 6679 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6679 & n is prime
  holds not n divides 6679 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
