1. (8 points) If the difference between two prime numbers is exactly 2, these two numbers are called a pair of twin primes.
For example: 3 and 5 are a pair of twin primes, 29 and 31 are also a pair of twin primes. In number theory research, twin primes are one of the hottest research topics. Chinese-American mathematician Yitang Zhang has made remarkable achievements in this field, and his story has inspired more young students to devote themselves to mathematical research. If the two prime numbers in a pair of twin primes do not exceed 200, the maximum sum of these two prime numbers is $\qquad$ .
【Solution】Solution: To find the maximum sum of prime numbers, start enumerating from the largest number. According to the rule that when the product is constant, one number being larger means the other is smaller.
199 is not a multiple of $2,3,5,7,11,17,19$, and if it had a factor greater than 19, it would certainly correspond to a smaller number, so 199 is a prime number.
197 is also verified to be a prime number in the same way.
The maximum sum is $199+197=396$.
Therefore, the answer is: 396.