
theorem
  6449 is prime
proof
  now
    6449 = 2*3224 + 1; hence not 2 divides 6449 by NAT_4:9;
    6449 = 3*2149 + 2; hence not 3 divides 6449 by NAT_4:9;
    6449 = 5*1289 + 4; hence not 5 divides 6449 by NAT_4:9;
    6449 = 7*921 + 2; hence not 7 divides 6449 by NAT_4:9;
    6449 = 11*586 + 3; hence not 11 divides 6449 by NAT_4:9;
    6449 = 13*496 + 1; hence not 13 divides 6449 by NAT_4:9;
    6449 = 17*379 + 6; hence not 17 divides 6449 by NAT_4:9;
    6449 = 19*339 + 8; hence not 19 divides 6449 by NAT_4:9;
    6449 = 23*280 + 9; hence not 23 divides 6449 by NAT_4:9;
    6449 = 29*222 + 11; hence not 29 divides 6449 by NAT_4:9;
    6449 = 31*208 + 1; hence not 31 divides 6449 by NAT_4:9;
    6449 = 37*174 + 11; hence not 37 divides 6449 by NAT_4:9;
    6449 = 41*157 + 12; hence not 41 divides 6449 by NAT_4:9;
    6449 = 43*149 + 42; hence not 43 divides 6449 by NAT_4:9;
    6449 = 47*137 + 10; hence not 47 divides 6449 by NAT_4:9;
    6449 = 53*121 + 36; hence not 53 divides 6449 by NAT_4:9;
    6449 = 59*109 + 18; hence not 59 divides 6449 by NAT_4:9;
    6449 = 61*105 + 44; hence not 61 divides 6449 by NAT_4:9;
    6449 = 67*96 + 17; hence not 67 divides 6449 by NAT_4:9;
    6449 = 71*90 + 59; hence not 71 divides 6449 by NAT_4:9;
    6449 = 73*88 + 25; hence not 73 divides 6449 by NAT_4:9;
    6449 = 79*81 + 50; hence not 79 divides 6449 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6449 & n is prime
  holds not n divides 6449 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
