Let's determine the number and sum of prime numbers less than 200, without the knowledge of prime numbers greater than 20, based solely on the fact that the number of prime numbers less than 105 is 27. (1 is not considered a prime number.)
Since the number of prime numbers less than 10 $(2,3,5,7)$ is 4, there are $27-4=23$ prime numbers between 10 and 105:

$$
11=p_{1}210-p_{2}>\ldots>210-p_{23}>105
$$

These numbers are either prime numbers or contain a prime factor greater than 7 but less than $\sqrt{210}$: 11 or 13. The latter numbers are as follows:

$$
\begin{aligned}
& 11 \cdot 11=121(=210-89) \\
& 11 \cdot 13=143(=210-67) \\
& 11 \cdot 17=187(=210-23) \\
& 13 \cdot 13=169(=210-41)
\end{aligned}
$$

The sum of these four numbers is: $121+143+187+169=620$.

The other 19 numbers under (1) are prime numbers because they are not divisible by any of the prime numbers 2, 3, 5, 7, 11, and 13. Furthermore, there are no other prime numbers between 105 and 200 besides these 19 numbers. If $p$ is a prime number between 105 and 200, then $2 \cdot 3 \cdot 5 \cdot 7-p$ is a number between 10 and 105, and if it has a prime factor, that factor cannot be greater than $7(<\sqrt{105})$, but this contradicts the fact that $p$ is a prime number greater than 105. Therefore, $210-p=p_{i}$ and thus $p=210-p_{i}$.

Therefore, the number of prime numbers less than 200 is:

$$
4+23+19=46
$$

The sum of these 46 prime numbers - since $p_{i}+210-p_{i}=210(i=1,2, \ldots, 23)-$

$$
2+3+5+7+23 \cdot 210-620=17+4830-620=4227
$$