User:Zuoweisx

As N approaches infinity, there's an infinite number of pairs of prime that make up even numbers around N

Even number 8: there are prime pairs: 3+5=8; is written as PP (8) = 1 Even number 10: there are two prime pairs: 3+7=10, 5+5=10; is written as PP (10) = 2 Even number 100: there are six prime pairs: 97+3=100, 89+11=100, 83+17=100, 71+29=100, 59+41=100, 53+47=100; is written as PP (100) = 6 Even number 999999998: can be composed of 1705025 prime pairs, PP(999999998)= 1705025 Even number 1000000000: can be composed of 2274205 prime number pairs, PP(1000000000)=2274205 As positive integer N approaches infinity, this is the rate at which PP(N) approaches infinity. Since the prime pair function is discrete and fluctuating, it is important to find a function that expresses the lower bound of the prime pair function. PPL(2n) = Pa - Pb According to Gauss 'prime number theorem P1(N) = N / Ln(N), Pa = n / Ln (n)  Pb=(2*n) / Ln(2*n) - n / Ln(n) write down N=2n，It has PPL(N)=N * { 1 / Ln(N / 2) – 1 / Ln(N) } We can also write as: PPL(N)=P1(N) * { Ln(2) / (Ln(N)-Ln(2) ) } When N is greater than 10, PPL(N) is an increasing function and greater than 1. The actual prime pairs function has a minimum value of 1, i.e. PP(4)=1; PP (6) = 1; PP (8) = 1; PP (12) = 1. In other words, even numbers greater than or equal to 4 can be written as the sum of two prime numbers (one prime pair), i.e.,  Goldbach conjecture is true.

The corollary is that the Goldbach conjecture is true.