
theorem
  6709 is prime
proof
  now
    6709 = 2*3354 + 1; hence not 2 divides 6709 by NAT_4:9;
    6709 = 3*2236 + 1; hence not 3 divides 6709 by NAT_4:9;
    6709 = 5*1341 + 4; hence not 5 divides 6709 by NAT_4:9;
    6709 = 7*958 + 3; hence not 7 divides 6709 by NAT_4:9;
    6709 = 11*609 + 10; hence not 11 divides 6709 by NAT_4:9;
    6709 = 13*516 + 1; hence not 13 divides 6709 by NAT_4:9;
    6709 = 17*394 + 11; hence not 17 divides 6709 by NAT_4:9;
    6709 = 19*353 + 2; hence not 19 divides 6709 by NAT_4:9;
    6709 = 23*291 + 16; hence not 23 divides 6709 by NAT_4:9;
    6709 = 29*231 + 10; hence not 29 divides 6709 by NAT_4:9;
    6709 = 31*216 + 13; hence not 31 divides 6709 by NAT_4:9;
    6709 = 37*181 + 12; hence not 37 divides 6709 by NAT_4:9;
    6709 = 41*163 + 26; hence not 41 divides 6709 by NAT_4:9;
    6709 = 43*156 + 1; hence not 43 divides 6709 by NAT_4:9;
    6709 = 47*142 + 35; hence not 47 divides 6709 by NAT_4:9;
    6709 = 53*126 + 31; hence not 53 divides 6709 by NAT_4:9;
    6709 = 59*113 + 42; hence not 59 divides 6709 by NAT_4:9;
    6709 = 61*109 + 60; hence not 61 divides 6709 by NAT_4:9;
    6709 = 67*100 + 9; hence not 67 divides 6709 by NAT_4:9;
    6709 = 71*94 + 35; hence not 71 divides 6709 by NAT_4:9;
    6709 = 73*91 + 66; hence not 73 divides 6709 by NAT_4:9;
    6709 = 79*84 + 73; hence not 79 divides 6709 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6709 & n is prime
  holds not n divides 6709 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
