
theorem
  277 is prime
proof
  now
    277 = 2*138 + 1; hence not 2 divides 277 by NAT_4:9;
    277 = 3*92 + 1; hence not 3 divides 277 by NAT_4:9;
    277 = 5*55 + 2; hence not 5 divides 277 by NAT_4:9;
    277 = 7*39 + 4; hence not 7 divides 277 by NAT_4:9;
    277 = 11*25 + 2; hence not 11 divides 277 by NAT_4:9;
    277 = 13*21 + 4; hence not 13 divides 277 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 277 & n is prime
  holds not n divides 277 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
