
theorem
  281 is prime
proof
  now
    281 = 2*140 + 1; hence not 2 divides 281 by NAT_4:9;
    281 = 3*93 + 2; hence not 3 divides 281 by NAT_4:9;
    281 = 5*56 + 1; hence not 5 divides 281 by NAT_4:9;
    281 = 7*40 + 1; hence not 7 divides 281 by NAT_4:9;
    281 = 11*25 + 6; hence not 11 divides 281 by NAT_4:9;
    281 = 13*21 + 8; hence not 13 divides 281 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 281 & n is prime
  holds not n divides 281 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
