
theorem
  571 is prime
proof
  now
    571 = 2*285 + 1; hence not 2 divides 571 by NAT_4:9;
    571 = 3*190 + 1; hence not 3 divides 571 by NAT_4:9;
    571 = 5*114 + 1; hence not 5 divides 571 by NAT_4:9;
    571 = 7*81 + 4; hence not 7 divides 571 by NAT_4:9;
    571 = 11*51 + 10; hence not 11 divides 571 by NAT_4:9;
    571 = 13*43 + 12; hence not 13 divides 571 by NAT_4:9;
    571 = 17*33 + 10; hence not 17 divides 571 by NAT_4:9;
    571 = 19*30 + 1; hence not 19 divides 571 by NAT_4:9;
    571 = 23*24 + 19; hence not 23 divides 571 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 571 & n is prime
  holds not n divides 571 by XPRIMET1:18;
  hence thesis by NAT_4:14;
