
theorem
  547 is prime
proof
  now
    547 = 2*273 + 1; hence not 2 divides 547 by NAT_4:9;
    547 = 3*182 + 1; hence not 3 divides 547 by NAT_4:9;
    547 = 5*109 + 2; hence not 5 divides 547 by NAT_4:9;
    547 = 7*78 + 1; hence not 7 divides 547 by NAT_4:9;
    547 = 11*49 + 8; hence not 11 divides 547 by NAT_4:9;
    547 = 13*42 + 1; hence not 13 divides 547 by NAT_4:9;
    547 = 17*32 + 3; hence not 17 divides 547 by NAT_4:9;
    547 = 19*28 + 15; hence not 19 divides 547 by NAT_4:9;
    547 = 23*23 + 18; hence not 23 divides 547 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 547 & n is prime
  holds not n divides 547 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
