[8] **viXra:1010.0064 [pdf]**
*submitted on 31 Oct 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 71 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This
is the Book proof. No great mathematicians study prime problems and prove Riemann
hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function
J_{2} (ω) we prove that the new prime theorems (791)-(840) contain infinitely many prime
solutions and no prime solutions. From (6) we are able to find the smallest solution
π_{k}(N_{0},2) ≥ 1. This is the Book theorem.

**Category:** Number Theory

[7] **viXra:1010.0049 [pdf]**
*submitted on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

We define a metasequence as a sequence constructed with the terms of other given sequence(s).
In this short note we present some open questions on concatenated primes involved in
metasequences.

**Category:** Number Theory

[6] **viXra:1010.0048 [pdf]**
*submitted on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 5 pages

We extend Kaprekar's Routine for a large class of applications. We also give particular examples
of this generalization as alternatives to Kaprekar's Routine and Number. Some open questions
about the length of the iterations until reaching either zero or a constant or a cycle, and about the
length of the cycles are asked at the end.

**Category:** Number Theory

[5] **viXra:1010.0043 [pdf]**
*submitted on 26 Oct 2010*

**Authors:** Nathaniel S. K. Hellerstein

**Comments:** 13 pages

In this article I generalize on a word problem by Bhaskaracharya. The resulting quadratics
are trivial to solve; but composing them, so that they have whole number solutions, is not
trivial. In this article I discover a class of sequences, which I call "Spade Sequences" as
homage to a hero of detective fiction, which generate both Bhaskaracharya quadratics and
their solutions. The article ends with a list of such word problems, presented as a problem
set with answer key.

**Category:** Number Theory

[4] **viXra:1010.0019 [pdf]**
*submitted on 9 Oct 2010*

**Authors:** Z. Wenpeng

**Comments:** 151 pages

This Book is devoted to the proceedings of the Sixth International Conference
on Number Theory and Smarandache Notions held in Tianshui during April 24-25,
2010. The organizers were myself and Professor Wangsheng He from Tianshui
Normal University. The conference was supported by Tianshui Normal University
and there were more than 100 participants. We had one foreign guest, Professor
K.Chakraborty from India. The conference was a great success and will give a
strong impact on the development of number theory in general and Smarandache
Notions in particular. We hope this will become a tradition in our country and will
continue to grow. And indeed we are planning to organize the seventh conference
in coming March which will be held in Weinan, a beautiful city of shaanxi.

**Category:** Number Theory

[3] **viXra:1010.0017 [pdf]**
*replaced on 16 Dec 2010*

**Authors:** Pankaj Mani

**Comments:** 5 pages

The Riemann hypothesis is proved to be true which states that all the non-trivial
zeros of Riemann zeta function lie along the line R(z)=1/2 for 0<R(z)<1.
The work done here clarifies that there is no need to find out the non-trivial zeros
of the Riemann zeta function to prove the Riemann hypothesis true as the
Riemann hypothesis must be true for the functional equation satisfied by the
zeta function to exist itself structurally in mathematics.

**Category:** Number Theory

[2] **viXra:1010.0006 [pdf]**
*replaced on 17 Oct 2010*

**Authors:** Alessandro Dallari

**Comments:** 46 pages

Some tools are discussed, in order to build power structures of primitive
roots in finite fields for any order q^{k}; relations between distinct roots
are deduced from m- and shift-and-add- sequences. Some heuristic computational
techniques, where information in a m- sequence is built from
below, are proposed. Full settlement is finally viewed in a physical scenario,
where a path leading to the Riemann Hypothesis can be enlighted.

**Category:** Number Theory

[1] **viXra:1010.0004 [pdf]**
*submitted on 1 Oct 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 71 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This
is the Book proof. No great mathematicians study prime problems and prove Riemann
hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function
J_{2} (ω) we prove that the new prime theorems (741)-(790) contain infinitely many prime
solutions and no prime solutions. From (6) we are able to find the smallest solution
π_{k}(N_{0},2) ≥ 1. This is the Book theorem.

**Category:** Number Theory