A few days ago, the Chinese mathematician Jiaweifeng made a breakthrough contribution to the study of Goldbach’s conjecture of 1+1 and twin prime number conjecture. His research and proof are like this:

**First, the proof of Goldbach’s conjecture 1+1 **

The conjecture wants to establish an even number equal to the addition of two prime numbers. The even number is limited and constrained by the prime number, which causes the division of the even range, and then determines the range of the conjecture. The even number is divided into even prime number 2 and infinite singular prime number. The even number of ≥ 6 must be taken in two odd prime numbers, and the even number added by two odd prime numbers must be an even number within the range of odd prime numbers. In odd numbers, only the range of odd prime numbers is suitable for the establishment of conjectures, proving that the conjecture is in odd prime numbers. The range is established, Is to solve the problem and prove it.

Odd numbers end with 1, 3, 5, 7, 9, even numbers end with 0, 2, 4, 6, 8, and any two odd numbers are added to 2n +1 +2 M +1 = 2(N + M +1), Subtraction is: 2n +1 -2m-1 = 2(n-m), obviously all are even numbers. Any two odd numbers can be added and subtracted as even numbers, because the odd prime numbers are both odd and prime numbers. Odd range, Obviously, the addition and subtraction of any two odd prime numbers are also even numbers. First, the subtraction results in P2-P1 = 2K, and P2 = P1 +2 K. Then the addition is P2 + P1 = P1 + P1 +2 K = 2(P1 + k) is even, such as: 3 +3 = 2(3 +0), 3 +5 = 2(3 +1), 5 +7 = 2(5 +1), etc. We call the even number obtained by adding any two odd prime numbers as an even number in the range of odd prime numbers. Since the number of odd prime numbers is infinite, the even number in the range of odd prime numbers is also infinite. Number, These even numbers can be seen as a set{xlx = P2 + P1, P1, P2 is any two of the odd prime numbers}, in which range all even numbers are obtained by adding any two odd prime numbers, so each even number can be written as The sum of two prime numbers, So Goldbach’s conjecture 1 +1 is established in the range of odd prime numbers. Any even number of ≥ 6 can be written as the sum of two prime numbers as long as it is an even number within the range of odd prime numbers.

**Second, twin prime guess proof**

The prime number conjecture is also a proposition about odd prime numbers. 3 and 5, 5 and 7, 11 and 13 are all odd prime numbers. I am proving Goldbach’s conjecture 1 +1. Any two singular prime number subtraction formulas have been obtained: P2-P1 = 2K, P2 = P1 +2 K, when K = 1, P2 = P1 +2, this result is exactly what the mathematician Aerfang Boliniyake expected.

Since the prime numbers are infinite, P2 and P1 are infinite variables, and P2 = P1 +2 is a binary primary function. In the coordinates, it is an infinitely extended straight line. All twin prime pairs are distributed on this straight line. This proves that the pair of twin prime numbers with a difference of 2 is infinite, that is, the twin prime number conjecture holds.

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