# Number Theory

## 1008 Submissions

 viXra:1008.0089 [pdf] submitted on 30 Aug 2010

### The New Prime Theorem (441)-(490)

Authors: Chun-Xuan Jiang

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J2(ω) we prove that the new prime theorems (441)-(490) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

 viXra:1008.0088 [pdf] submitted on 31 Aug 2010

### Goldbach' Conjecture (9): Proved Hardy-Littlewood Conjecture (A)

Authors: Tong Xin Ping
Comments: 4 pages, In Chinese

We have inclusion-exclusion formula of π(N) and inclusion-exclusion formula of r2(N). Make use of inclusion-exclusion formula, we can obtain Hardy-Littlewood Conjecture (A).
Category: Number Theory

 viXra:1008.0087 [pdf] submitted on 30 Aug 2010

### The New Prime Theorem (541)-(590)

Authors: Chun-Xuan Jiang

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J2(ω) we prove that the new prime theorems (541)-(590) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

 viXra:1008.0086 [pdf] submitted on 30 Aug 2010

### The New Prime Theorem (491)-(540)

Authors: Chun-Xuan Jiang

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J2(ω) we prove that the new prime theorems (491)-(540) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

 viXra:1008.0082 [pdf] submitted on 13 Mar 2010

### A Set of Conjectures on Smarandache Sequences

Authors: Sylvester Smith

Searching through the Archives of the Arizona State University, I found interesting sequences of numbers and problems related to them. I display some of them, and the readers are welcome to contribute with solutions or ideas.
Category: Number Theory

 viXra:1008.0080 [pdf] submitted on 27 Aug 2010

### The New Prime Theorem (391)-(440)

Authors: Chun-Xuan Jiang

Using Jiang function we prove that the new prime theorems (391)-(440) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory

 viXra:1008.0069 [pdf] submitted on 25 Aug 2010

### Wandering in the World of Smarandache Numbers

Authors: A.A.K. Majumdar

It was in mid-nineties of the last century when I received a letter from Professor Ion Patrascu of the Fratii Buzesti College, Craiova, Romania, with lots of enclosures, introducing me with this new branch of Mathematics. Though my basic undergraduate degree is in Mathematics, my research field at that time was Operations Research and Mathematical Programming.
Category: Number Theory

 viXra:1008.0064 [pdf] submitted on 23 Aug 2010

### Goldbach' Conjecture (8): Upper Bound Estimation of Number of Goldbach' Primes

Authors: Tong Xin Ping
Comments: 3 pages, In Chinese

This upper bound estimation prevailed over upper bound estimation of Chen Jing Run
Category: Number Theory

 viXra:1008.0062 [pdf] submitted on 22 Aug 2010

### Smarandache Consecutive Prime Sequences (n = 1 to 100)

Authors: Robert G. Wilson V

"Smarandache consecutive sequences" is the nth member of the consecutive sequence, e. g. Sm(11)=1234567891011, and RSm(11)=1110987654321. Following is the prime version of "Smarandache consecutive sequences"
Category: Number Theory

 viXra:1008.0061 [pdf] submitted on 22 Aug 2010

### Some Properties of the Pseudo-Smarandache Function

Authors: Richard Pinch

Charles Ashbacher  has posed a number of questions relating to the pseudo-Smarandache function Z(n). In this note we show that the ratio of consecutive values Z(n + 1)/Z(n) and Z(n - 1)/Z(n) are unbounded; that Z(2n)/Z(n) is unbounded; that n/Z(n) takes every integer value infinitely often; and that the series Σn 1/Z(n)α is convergent for any α > 1.
Category: Number Theory

 viXra:1008.0054 [pdf] submitted on 20 Aug 2010

### Goldbach' Conjecture (7): Five Proofs that is Under Five Assumptions Term

Authors: Tong Xin Ping
Comments: 4 pages, In Chinese

According to five assumptions, get five proofs
Category: Number Theory

 viXra:1008.0036 [pdf] submitted on 12 Aug 2010

### On the Distribution of Prime Numbers in the Intervals Defined by the Fibonacci Numbers

Authors: J. S. Markovitch

The number of primes in the inclusive intervals defined by consecutive Fibonacci numbers exhibits interesting behavior between the Fibonacci numbers 55 and 196418. Specifically, starting with the interval [55, 89] through the interval [121393,196418] the ratio of the number of primes in successive intervals is a value that alternates high, low, high, low, etc.
Category: Number Theory

 viXra:1008.0022 [pdf] replaced on 29 Nov 2011

### A Short Proof of Fermat's Last Theorem

Authors: Morgan D. Rosenberg

Presented herein is a proof of Fermat's Last Theorem, which is not only short (relative to Wiles' 109 page proof), but is also performed using relatively elementary mathematics. Particularly, the binomial theorem is utilized, which was known in the time of Fermat (as opposed to the elliptic curves of Wiles' proof, which belong to modern mathematics). Using the common integer expression an + bn = cn for Fermat's Last Theorem, the substitutions c = b+i and b = a+j are made, where i and j are integers. Using a Taylor expansion (i.e., in the form of the binomial theorem), Fermat's Last Theorem reduces to (see paper) and what remains to be proven, from this equation, is that (see paper) only has rational solutions for n=1 and n=2. This proof is presented herein, thus proving that an + bn = cn only has integer solutions for a, b and c for integer values of the exponent n=1 or n=2.
Category: Number Theory

 viXra:1008.0021 [pdf] submitted on 8 Aug 2010

### The Philosophy Error of the "Almost Prime"

Authors: Tong Xin Ping
Comments: 2 pages, In Chinese

Don't confuse quantitative change and qualitative change.
Category: Number Theory

 viXra:1008.0006 [pdf] submitted on 4 Aug 2010

### The Philosophy Error of the Proposition "9+9"~"1+2"

Authors: Tong Xin Ping
Comments: 2 Pages. In Chinese

The method of the quantitative change can not solve the problem of the qualitative change.
Category: Number Theory

 viXra:1008.0001 [pdf] replaced on 20 Nov 2010

### The Theory About Infinity of Simple Numbers-Twins

Authors: Valery Demidovich
Comments: v2 is 29 Pages in Russian, v3 is 28 pages in English

The work maintenance: attempt to solve a problem about definition of set of simple numbers-twins is made. In work absolutely new approach which is based on algorithm of a sieve of Eratosfena is applied.
Category: Number Theory