1. Game prime conjecture
The conjecture of lifetime prime number is a conjecture about prime number put forward by Liu Foqing. According to this conjecture, there are infinitely many prime numbers in the form of 2 n- 1, where n is a positive integer. This conjecture has some similarities with mersenne prime, but it is not exactly the same. Although we have found some prime numbers that satisfy the game prime number conjecture, such as 3, 7, 3 1 and so on. So far, we haven't got a strict proof of this conjecture.
2. Odd complex formula
The formula of odd composite number is a formula about odd composite number put forward by Liu Foqing. The so-called odd number refers to an odd number greater than 1, which can be expressed as the product of two natural numbers. The odd complex formula gives a method to solve odd complex numbers. The specific formula is: let the odd number be n = 2 k * m+ 1, where k is a non-negative integer and m is a positive integer, then n is odd if and only if any integer A meets the following conditions: a (n- 1) ≡ 1 (mod n).
3. Knowledge of number theory
In order to better understand Yi Sheng's prime conjecture and odd complex formula, we need to know some knowledge of number theory. Number theory is a branch of mathematics that studies integers and their properties. It is closely related to prime number, factor, prime number and congruence.
In number theory, a prime number refers to an integer that can only be divisible by 1 and itself, while a composite number refers to an integer that can be divisible by other integers except 1 and itself. Congruence is an important concept in number theory, which means that the remainder obtained by dividing two integers by the same number is equal. The study of number theory is of great significance for understanding Yi Sheng's prime conjecture and odd complex formula.
4. Current progress and challenges
At present, the proof of prime conjecture and odd formula is still in progress. Although some prime numbers have been found that satisfy the conjecture of game prime numbers, and the odd composite formula also explains the properties of odd composite numbers to some extent, there is still a lack of strict proof.
One of the difficulties in proving the game prime conjecture is how to prove that a number with the shape of 2 n- 1 is a prime number at the infinite value of n. The proof of odd complex formula needs to study the concepts of congruence in number theory and find a more rigorous proof method.
summary
Life-long prime conjecture and odd complex number formula are conjectures and formulas about prime numbers and odd complex numbers put forward by Liu Foqing. These problems involve important concepts and methods in number theory, and it is still a challenge to prove them. To solve these problems, we need to further study the knowledge of number theory and explore more rigorous proof methods.