
theorem
  5443 is prime
proof
  now
    5443 = 2*2721 + 1; hence not 2 divides 5443 by NAT_4:9;
    5443 = 3*1814 + 1; hence not 3 divides 5443 by NAT_4:9;
    5443 = 5*1088 + 3; hence not 5 divides 5443 by NAT_4:9;
    5443 = 7*777 + 4; hence not 7 divides 5443 by NAT_4:9;
    5443 = 11*494 + 9; hence not 11 divides 5443 by NAT_4:9;
    5443 = 13*418 + 9; hence not 13 divides 5443 by NAT_4:9;
    5443 = 17*320 + 3; hence not 17 divides 5443 by NAT_4:9;
    5443 = 19*286 + 9; hence not 19 divides 5443 by NAT_4:9;
    5443 = 23*236 + 15; hence not 23 divides 5443 by NAT_4:9;
    5443 = 29*187 + 20; hence not 29 divides 5443 by NAT_4:9;
    5443 = 31*175 + 18; hence not 31 divides 5443 by NAT_4:9;
    5443 = 37*147 + 4; hence not 37 divides 5443 by NAT_4:9;
    5443 = 41*132 + 31; hence not 41 divides 5443 by NAT_4:9;
    5443 = 43*126 + 25; hence not 43 divides 5443 by NAT_4:9;
    5443 = 47*115 + 38; hence not 47 divides 5443 by NAT_4:9;
    5443 = 53*102 + 37; hence not 53 divides 5443 by NAT_4:9;
    5443 = 59*92 + 15; hence not 59 divides 5443 by NAT_4:9;
    5443 = 61*89 + 14; hence not 61 divides 5443 by NAT_4:9;
    5443 = 67*81 + 16; hence not 67 divides 5443 by NAT_4:9;
    5443 = 71*76 + 47; hence not 71 divides 5443 by NAT_4:9;
    5443 = 73*74 + 41; hence not 73 divides 5443 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5443 & n is prime
  holds not n divides 5443 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
