
theorem
  6469 is prime
proof
  now
    6469 = 2*3234 + 1; hence not 2 divides 6469 by NAT_4:9;
    6469 = 3*2156 + 1; hence not 3 divides 6469 by NAT_4:9;
    6469 = 5*1293 + 4; hence not 5 divides 6469 by NAT_4:9;
    6469 = 7*924 + 1; hence not 7 divides 6469 by NAT_4:9;
    6469 = 11*588 + 1; hence not 11 divides 6469 by NAT_4:9;
    6469 = 13*497 + 8; hence not 13 divides 6469 by NAT_4:9;
    6469 = 17*380 + 9; hence not 17 divides 6469 by NAT_4:9;
    6469 = 19*340 + 9; hence not 19 divides 6469 by NAT_4:9;
    6469 = 23*281 + 6; hence not 23 divides 6469 by NAT_4:9;
    6469 = 29*223 + 2; hence not 29 divides 6469 by NAT_4:9;
    6469 = 31*208 + 21; hence not 31 divides 6469 by NAT_4:9;
    6469 = 37*174 + 31; hence not 37 divides 6469 by NAT_4:9;
    6469 = 41*157 + 32; hence not 41 divides 6469 by NAT_4:9;
    6469 = 43*150 + 19; hence not 43 divides 6469 by NAT_4:9;
    6469 = 47*137 + 30; hence not 47 divides 6469 by NAT_4:9;
    6469 = 53*122 + 3; hence not 53 divides 6469 by NAT_4:9;
    6469 = 59*109 + 38; hence not 59 divides 6469 by NAT_4:9;
    6469 = 61*106 + 3; hence not 61 divides 6469 by NAT_4:9;
    6469 = 67*96 + 37; hence not 67 divides 6469 by NAT_4:9;
    6469 = 71*91 + 8; hence not 71 divides 6469 by NAT_4:9;
    6469 = 73*88 + 45; hence not 73 divides 6469 by NAT_4:9;
    6469 = 79*81 + 70; hence not 79 divides 6469 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6469 & n is prime
  holds not n divides 6469 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
