
theorem
  5449 is prime
proof
  now
    5449 = 2*2724 + 1; hence not 2 divides 5449 by NAT_4:9;
    5449 = 3*1816 + 1; hence not 3 divides 5449 by NAT_4:9;
    5449 = 5*1089 + 4; hence not 5 divides 5449 by NAT_4:9;
    5449 = 7*778 + 3; hence not 7 divides 5449 by NAT_4:9;
    5449 = 11*495 + 4; hence not 11 divides 5449 by NAT_4:9;
    5449 = 13*419 + 2; hence not 13 divides 5449 by NAT_4:9;
    5449 = 17*320 + 9; hence not 17 divides 5449 by NAT_4:9;
    5449 = 19*286 + 15; hence not 19 divides 5449 by NAT_4:9;
    5449 = 23*236 + 21; hence not 23 divides 5449 by NAT_4:9;
    5449 = 29*187 + 26; hence not 29 divides 5449 by NAT_4:9;
    5449 = 31*175 + 24; hence not 31 divides 5449 by NAT_4:9;
    5449 = 37*147 + 10; hence not 37 divides 5449 by NAT_4:9;
    5449 = 41*132 + 37; hence not 41 divides 5449 by NAT_4:9;
    5449 = 43*126 + 31; hence not 43 divides 5449 by NAT_4:9;
    5449 = 47*115 + 44; hence not 47 divides 5449 by NAT_4:9;
    5449 = 53*102 + 43; hence not 53 divides 5449 by NAT_4:9;
    5449 = 59*92 + 21; hence not 59 divides 5449 by NAT_4:9;
    5449 = 61*89 + 20; hence not 61 divides 5449 by NAT_4:9;
    5449 = 67*81 + 22; hence not 67 divides 5449 by NAT_4:9;
    5449 = 71*76 + 53; hence not 71 divides 5449 by NAT_4:9;
    5449 = 73*74 + 47; hence not 73 divides 5449 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5449 & n is prime
  holds not n divides 5449 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
