Abstract
In this article, we use set, function, sieve and number theory to study the prime and composite numbers, prove that the lower limit formula of the number of prime numbers derived from the Euler’s function, and find d(n) to count the lower limit formula of the number of prime integer-pairs. We proved that Goldbach’s conjecture is correct by mathematical induction. Finally, we proved proof reliance by mathematical analysis and computer data.
Highlights
Goldbach’s conjecture is one of the oldest and best-known unsolved problems in number theory
In the letter to Euler by Goldbach in 1742, Goldbach put forward the following conjecture: any even number greater than 2 can be written as the sum of two prime numbers
In order to obtain a definite lower limit of the number of primes and simple operation, we find a function that may be associated with the error as an error compensation
Summary
Goldbach’s conjecture is one of the oldest and best-known unsolved problems in number theory. It states: every even integer greater than 2 can be expressed as the sum of two primes [1] [3]. We know the number of primes can calculate by sieve of Eratosthenes and inclusion exclusion formula [3] [5] [6]. It can be received exact value by the calculation of the tolerance formula, but it can only be used in small range of positive integers, because the operation is very complicated. For a larger range of data operations, there is inefficiency
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