# Number Theory

## 0904 Submissions

[2] **viXra:0904.0003 [pdf]**
*submitted on 7 Apr 2009*

### On The Consecutive Integers n+i-1 = (i+1)P_{i}

**Authors:** Chun-Xuan Jiang

**Comments:** recovered from sciprint.org

By using the Jiang's function J_{2}(ω) we prove that there exist infinitely many integers n such
that n = 2P_{1}, n+1 = 3P_{2}, ..., n+k-1 = (k+1)P_{k} are all composites for arbitrarily
long k, where P_{1}, P_{2}, ..., P_{k} are all
primes. This result has no prior occurrence in the history of number theory.

**Category:** Number Theory

[1] **viXra:0904.0001 [pdf]**
*submitted on 6 Apr 2009*

### On the Foundamental Theorem in Arithmetic Progession of Primes

**Authors:** Chun-Xuan Jiang

**Comments:** recovered from sciprint.org

Using Jiang function we prove the foundamental theorem in arithmetic progression of primes.
The primes contain only k < P_{g+1} long arithmetic progressions, but the primes have no k > P_{g+1} long
arithmetic progressions. Terence Tao is recipient of 2006 Fields medal. Green and Tao proved
that the primes contain arbitrarily long arithmetic progressions which is absolutely false.
They do not understand the arithmetic progression of primes.

**Category:** Number Theory