
theorem
  271 is prime
proof
  now
    271 = 2*135 + 1; hence not 2 divides 271 by NAT_4:9;
    271 = 3*90 + 1; hence not 3 divides 271 by NAT_4:9;
    271 = 5*54 + 1; hence not 5 divides 271 by NAT_4:9;
    271 = 7*38 + 5; hence not 7 divides 271 by NAT_4:9;
    271 = 11*24 + 7; hence not 11 divides 271 by NAT_4:9;
    271 = 13*20 + 11; hence not 13 divides 271 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 271 & n is prime
  holds not n divides 271 by XPRIMET1:12;
  hence thesis by NAT_4:14;
