The symmetry theorem of prime numbers, also known as the homogeneous theorem, means that in natural numbers, every prime number greater than three has at least one group of mutually symmetric prime numbers as symmetry points, that is, the distances to the number are equal.

Someone has done this calculation:12+1+41= 43, 2 2+2+4 1 = 47, 3 2+3+4 1 = 53 ...........................................................................'s formula holds up until n=39. But when n=40, the formula is invalid, because 40 2+40+41=1681= 41* 41.

In this range, it is a series, which naturally holds. But it is more difficult to prove later.

In the17th century, there was a French mathematician named Mei Sen. He once made a guess: 2 p- 1 algebraic expression, when p is a prime number, 2 p- 1 is a prime number. He checked that when p=2, 3, 5, 7, 17, 19, the values of the algebraic expressions obtained are all prime numbers. Later Euler proved that when p=3 1, 2 p- 1 is a prime number. When p = 2,3,5,7, Mp is a prime number, but M 1 1 = 2047 = 23× 89 is not a prime number.

Now there are three Mason numbers left, p=67,127,257, which have not been verified for a long time because they are too big. 250 years after Mei Sen's death, American mathematician Kohler proved that 267-1=193707721* 761838257287 is a composite number. This is the ninth Mei Sen number. In the 20th century, people successively proved that 10 Mason number is a prime number and 1 1 Mason number is a composite number. The disordered arrangement of prime numbers also makes it difficult for people to find the law of prime numbers. This theorem has been proved, but the process may not be published in the paper.

So I can't find it, and a lot of math can't prove it. How do these people prove it?