
theorem
  131 is prime
proof
  now
    131 = 2*65 + 1; hence not 2 divides 131 by NAT_4:9;
    131 = 3*43 + 2; hence not 3 divides 131 by NAT_4:9;
    131 = 5*26 + 1; hence not 5 divides 131 by NAT_4:9;
    131 = 7*18 + 5; hence not 7 divides 131 by NAT_4:9;
    131 = 11*11 + 10; hence not 11 divides 131 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 131 & n is prime
  holds not n divides 131 by XPRIMET1:10;
  hence thesis by NAT_4:14;
end;
