[6] **viXra:1203.0075 [pdf]**
*submitted on 2012-03-19 10:44:15*

**Authors:** Louis D. Grey

**Comments:** 3 Pages.

It is a well known result that for a prime of the form 4k+3, there are more quadratic residues than non-residues in the interval (1,(p-1)/2). Using elementary methods,we provide an asymptotic estimate for the number of residues in the interval.

**Category:** Number Theory

[5] **viXra:1203.0073 [pdf]**
*submitted on 2012-03-19 11:47:19*

**Authors:** Louis D. Grey

**Comments:** Pages. Remove word "louis" after title of paper

We prove a special case of C.L. Siegel's theorem regarding the class number of binary quadratic forms with fundamental discriminant -D<0.

**Category:** Number Theory

[4] **viXra:1203.0064 [pdf]**
*replaced on 2017-09-10 09:26:00*

**Authors:** Ricardo G. Barca

**Comments:** 43 Pages. Extended explanation in the Introduction.

The binary Goldbach conjecture asserts that every even integer greater than 4 is the sum of two primes. In order to prove this statement, we start by defining a kind of double sieve of Eratosthenes as follows. Given an even integer x, we sift out from [1, x] all those elements that are congruents to 0 modulo p, or congruents to x modulo p, where p is a prime less than the square root of x. So, any integer in the interval [sqrt{x}, x] that remains unsifted is a prime p for which either x-p = 1 or x-p is also a prime. Then, we introduce a new way to formulate this sieve, which we call the sequence of k-tuples of remainders. Using this tool, we obtain a lower bound for the number of elements in [1, x] that survives the sifting process. We prove, for every even number x greater than the square of 149, that there exist at least 3 integers in the interval [ 1, x ] that remains unsifted. This proves the binary Goldbach conjecture for every even number x greater than the square of 149, which is our main result.

**Category:** Number Theory

[3] **viXra:1203.0060 [pdf]**
*submitted on 2012-03-16 02:45:52*

**Authors:** Chun-Xuan Jiang

**Comments:** 90 Pages. It is the very important paper for number theory

Using Jiang function we prove the new prime theorems(1441)-(1480).

**Category:** Number Theory

[2] **viXra:1203.0050 [pdf]**
*submitted on 2012-03-14 19:21:00*

**Authors:** Chun-Xuan Jiang

**Comments:** 90 Pages.

using Jiang function we prove the new prime theorems(1491)-��1540��

**Category:** Number Theory

[1] **viXra:1203.0019 [pdf]**
*replaced on 2012-03-06 19:53:44*

**Authors:** Chun-Xuan Jiang

**Comments:** 5 Pages.

All eyes are on the Riemann hypothesis,zeta and L-functions ,which are false ,please read this paper.

**Category:** Number Theory