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The distributive law of odd primes in the natural numbers Even number E≥6 can be expressed as the sum of two odd primes
Goldbach hypothesis odd prime infimum
2015/6/2
1. This paper provided the distributive law of odd primes in the natural numbers. 2. Given a mathematical model of two opposite directional sequences of natural numbers： ︳Omin ,…，…,…，Omax ︳ ︳Omax ,…, ...
The distributive law of primes in the natural numbers Even numbers 2x≥6 can be expressed as the sum of two primes
Goldbach hypothesis prime infimum
2015/6/2
Find out the distributive law of primes in the natural numbers. By means of the distributive law of primes we show that even numbers 2x≥6 can be expressed as the sum of two primes.
Congruences of Multipartition Functions Modulo Powers of Primes
modular form partition multipartition Ramanujan-type congruence
2014/6/3
Let pr(n) denote the number of r-component multipartitions of n, and let Sγ λ be the space spanned by η(24z)γφ(24z), where η(z) is the Dedekind’s eta function and η(z) is a holomorphic modular form i...
The distributive law of primes and the proof of Goldbach hypothesis
Goldbach hypothesis supremum infimum prime in pairs p1＋p2
2015/6/2
This paper concerns a graph of (3≤x≤2500, N) orthogonal coordinate system. 1. Distributive law of primes, (x/㏒x)㏒e＜π(x)≤(x/㏒x)㏒199/19, (3≤x＜∞); 2. ①. Folding expression of odd numbers, (x＝2n－1), ︱x,…,...
Proof of hypothesis of twin primes (important step: choosing a suitable interval)
Twin primes supremum infimum
2015/6/2
1. Distributive law of primes: (x/㏒x)㏒e＜π(x)≤(x/㏒x) ㏒11330／113, (11≤x＜∞); 2. Shortest suitable interval, [11, 19]; 3. Expression of twin odd numbers, ︱2x－11,…,…,…,4x－27︱ ︱2x－ 9,…,…,…,4x－25︱, Number of...
In this paper we bring into attention an old subject in number theory. Fermat showed that a prime can be written as a sum of two squares if and only if it is a multiple of four plus one and the decomp...
A Diophantine problem with a prime and three squares of primes
Goldbach-type theorems Hardy-Littlewood method diophantine inequalities
2012/6/14
We prove that if $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ are non-zero real numbers, not all of the same sign, $\lambda_1 / \lambda_2$ is irrational, and $\varpi$ is any real number then,...
In the present work we investigate the largest possible gaps between consecutive numbers which can be written as the difference of two primes. The best known upper bounds are the same as those concern...
Mersenne Primes in Real Quadratic Fields
Mersenne Primes Real Quadratic Fields Number Theory
2012/5/24
The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\sqrt{2})$ is studied in detail with a focus on representing Mersenn...
Every prime larger than 3 is arithmetic mean of other two primes
prime distribution of primes arithmetic progression Goldbach conjecture
2011/9/21
In this paper a new stronger proposition has been advanced and shown, that is, every prime larger than 3 is arithmetic mean of other two primes, and other important propositions that there are infinit...
The irregular distribution of primes up to 300,000 in the sequence of odd numbers
prime distribution of primes
2011/9/19
In this paper we listed a sequence of odd numbers up to 300,000 by a computer calculating and it could be find that the density of prime numbers is decreased as odd number increases and that there exi...
There are infinitely many primes of the form a^2 +1
primes in polynomials sieve method limit of sequences Godel completeness theorem Ross-Littwood paradoxset
2011/9/18
In this paper we founded a formal system of second order arithmetic $\langle P(N), +, \times, 0, 1, \in \rangle$ by extending the operations $+, \times$ on natural numbers to the operations on finite ...
Minimal primes of ideals arising from conditional independence statements
conditional independence statements Commutative Algebra
2011/9/22
Abstract: We consider ideals, arising in the context of conditional independence models, that generalize those considered by Fink [6] in a way distinct from the generalization of [11]. We describe the...
Lower bounds for finiteness of generalized local cohomology modules and their associated primes
Generalized local cohomology modules associatted prime Serre subcategories
2011/9/20
Abstract: Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. In this paper, we study relations between f...
Abstract: We consider the second of Mullin's sequences of prime numbers related to Euclid's proof that there are infinitely many primes. We show in particular that it omits infinitely many primes, con...