In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, when n ≥ k - 1, there always e...In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, when n ≥ k - 1, there always exists at least a prime number p such that kn p ≤ (k +1)n. The Bertrand-Chebyshev’s theorem is a special case of this theorem when k = 1. In the field of prime number distribution, just as the prime number theorem provides the approximate number of prime numbers relative to natural numbers, while the new theory indicates that prime numbers exist in the specific intervals between natural numbers, that is, the new theorem provides the approximate positions of prime numbers among natural numbers.展开更多
The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is dis...The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is discussed. Through the corresponding prime distribution rate of integers and composite numbers, it is found that the corresponding prime distribution rate of composite numbers approaches the corresponding prime distribution rate of integers. The distribution principle of corresponding prime number of composite number is proved. The twin prime distribution theorem is obtained. The number of twin prime numbers is thus obtained. It provides a practical way to study the conjecture of twin prime numbers.展开更多
In this paper the functional-differential equation of the distribution of primenumbers derived by de Visme [4] is strdied in details. It is proved that there existinfinitely many solutions of this equation , and all p...In this paper the functional-differential equation of the distribution of primenumbers derived by de Visme [4] is strdied in details. It is proved that there existinfinitely many solutions of this equation , and all positive strong solutions andpositive solutions of the Cauchy problem behave very much like the distrbutionfunction of prime numbers. The results are complementary to Driver [1] andwright [3].展开更多
The famous conjecture in distribution of prime numbers remains unsolved whether there exists a constant inequality of “ π(x+y)≤π(x)+π(y) ” for all integers such as x, y≥2. The present article argues that when x...The famous conjecture in distribution of prime numbers remains unsolved whether there exists a constant inequality of “ π(x+y)≤π(x)+π(y) ” for all integers such as x, y≥2. The present article argues that when x>11, y≤30, there always is a constant tenable inequality.展开更多
文摘In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, when n ≥ k - 1, there always exists at least a prime number p such that kn p ≤ (k +1)n. The Bertrand-Chebyshev’s theorem is a special case of this theorem when k = 1. In the field of prime number distribution, just as the prime number theorem provides the approximate number of prime numbers relative to natural numbers, while the new theory indicates that prime numbers exist in the specific intervals between natural numbers, that is, the new theorem provides the approximate positions of prime numbers among natural numbers.
文摘The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is discussed. Through the corresponding prime distribution rate of integers and composite numbers, it is found that the corresponding prime distribution rate of composite numbers approaches the corresponding prime distribution rate of integers. The distribution principle of corresponding prime number of composite number is proved. The twin prime distribution theorem is obtained. The number of twin prime numbers is thus obtained. It provides a practical way to study the conjecture of twin prime numbers.
文摘In this paper the functional-differential equation of the distribution of primenumbers derived by de Visme [4] is strdied in details. It is proved that there existinfinitely many solutions of this equation , and all positive strong solutions andpositive solutions of the Cauchy problem behave very much like the distrbutionfunction of prime numbers. The results are complementary to Driver [1] andwright [3].
文摘The famous conjecture in distribution of prime numbers remains unsolved whether there exists a constant inequality of “ π(x+y)≤π(x)+π(y) ” for all integers such as x, y≥2. The present article argues that when x>11, y≤30, there always is a constant tenable inequality.
