
theorem
  181 is prime
proof
  now
    181 = 2*90 + 1; hence not 2 divides 181 by NAT_4:9;
    181 = 3*60 + 1; hence not 3 divides 181 by NAT_4:9;
    181 = 5*36 + 1; hence not 5 divides 181 by NAT_4:9;
    181 = 7*25 + 6; hence not 7 divides 181 by NAT_4:9;
    181 = 11*16 + 5; hence not 11 divides 181 by NAT_4:9;
    181 = 13*13 + 12; hence not 13 divides 181 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 181 & n is prime
  holds not n divides 181 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
