Guiguzi's examination of apprentices is a classic old topic, which can show a person's level of mathematical thinking.

The voice numbers are S 1, P 1, S2.

Let these two numbers be x, y, and s, product p.

Judging from S 1, P doesn't know these two numbers, so S can't be obtained by adding two prime numbers, S < = 4 1, because if S > 4 1, then P can definitely guess if it gets 4 1× (S-4 1). So the sum S is one of {1 1, 17, 23, 27, 29, 35, 37, 4 1}, and let this set be a.

1). Suppose the sum is 1 1. 11= 2+9 = 3+8 = 4+7 = 5+6. If P gets 18, 18 = 3× 6 = 2× 9, and only 2+9 falls in the set A, then P can be said to be P.

Let's see, if P gets 24,24 = 6× 4 = 3× 8 = 2×12, P can also say P 1, because in at least two cases P can say P 1, so A can't assert s 2, so the sum is not1/kloc.

2). Suppose the sum is 17. 17 = 2+ 15 = 3+ 14 = 4+ 13 = 5+ 12 = 6+ 1 1 = 7+ 10 = 8+

3). Suppose the sum is 23. 23 = 2+2 1 = 3+20 = 4+ 19 = 5+ 18 = 6+ 17 = 7+ 16 = 8+ 15 = 9+65438.

4). Suppose the sum is 27. If p gets 8× 19 or 4×23, it can be asserted that P 1, so the sum is not 27.

5). Suppose the sum is 29. If p gets 13× 16 or 7×22, it can be asserted that P 1, so the sum is not 29.

6). Suppose the total number is 35. If p gets 16× 19 or 4×3 1, it can be asserted that P 1, so the sum is not 35.

7). Suppose the sum is 37. If p gets 8×29 or 1 1×26, it can be asserted that P 1, so the sum is not 37.

8). Suppose the sum is 4 1. If b gets 4×37 or 8×33, it can be asserted that P 1, so the sum is not 4 1.

To sum up, these two numbers are 4 and 13.

Extended data:

Guiguzi, who was active from the late Spring and Autumn Period to the Warring States Period, was called a native of East Zhou Weiguo. He lived for a hundred years and then disappeared. He entered the Ghost Valley of Yunmeng Mountain in Qingxi all the year round to collect herbs and cultivate monasteries. Is an extremely mysterious figure in the history of China!

Guiguzi is full of profound knowledge, not only knowing the mysteries of the natural universe, but also knowing that a hundred schools of thought contend! Guiguzi has trained many elites, such as Su Qin, Zhang Yi, Sun Bin and Pang Juan. These disciples were all unknown before they entered the mountain, but after they came out, they all shined brilliantly, and their fame was eternal!

Among all the families, the achievements of military strategists and strategists are the most remarkable and well known! "As for the military representative, there is nothing wrong with the white war, and Wang Jian swept the six countries. On the representative figures of military strategists: the words of one person are more important than the treasure of Jiuding. A three-inch tongue is better than a million masters! "

Great historians Su Qin, Zhang Yi and Sima Qian solemnly wrote in Historical Records: "These two people are really dangerous!" A smile makes the world prosperous, and an anger makes the prince afraid. Mencius and Teng Wengong. This shows that Ghost Valley is so powerful!

There are many experts in Ghost Valley, and all of them have established immortal achievements: Pang Juan is proud of sheep, Sun Bin is unbeaten in all battles, the Soviet Union is the seal of the six countries, and Zhang Yi is the prime minister of Qin twice; There is also Shang Yang Li Si, one is to reform filial piety, and the other is to help the first emperor unify mountains and rivers!

As for Xu Fu who later crossed the border to Japan, it is said that he became the first emperor of Japan: Emperor Jimmu. Now Japanese folk temples are worshipping, and many Japanese even publicly claim that they are descendants of Xu Fu, leaving the genealogy of the Xu family for reading.