67. $x$ is a positive rational number, $(x)$ represents the number of prime numbers not exceeding $x$, for example, $(5)=3$, meaning there are 3 prime numbers not exceeding 5, which are 2, 3, 5. Therefore, $(x)$ defines an operation on $x$. Then $((20) \times(1)+(7))$ is $\qquad$
Answer: 2.
Solution: $(x)$ defines an operation for positive rational numbers $x$. The steps of the operation are:
(1) Write down the sequence of natural numbers not exceeding $x$;
(2) Mark the prime numbers in this sequence;
(3) Count the number of these prime numbers.

According to the above operation method, we calculate $((20) \times(1)+(7))$.
Since
$(20)=8$
(1) $=0$,
(7) $=4$,

Therefore,
$$
((20) \times(1)+(7))=(8 \times 0+4)=(4)=2 \text{. }
$$