Number Theory

0904 Submissions

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

On The Consecutive Integers n+i-1 = (i+1)Pi

Authors: Chun-Xuan Jiang
Comments: recovered from sciprint.org

By using the Jiang's function J2(ω) we prove that there exist infinitely many integers n such that n = 2P1, n+1 = 3P2, ..., n+k-1 = (k+1)Pk are all composites for arbitrarily long k, where P1, P2, ..., Pk 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 < Pg+1 long arithmetic progressions, but the primes have no k > Pg+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