[21] **viXra:1009.0058 [pdf]**
*submitted on 19 Sep 2010*

**Authors:** Moon Kyom

**Comments:** 9 pages

Added the infinite sign and the infinitesimal sign and defined an operation.
The infinite calculation of number became possible.
The benefits gained by infinite number is as follows.

**Category:** Number Theory

[20] **viXra:1009.0049 [pdf]**
*submitted on 14 Sep 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 70 pages

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 J_{2}(ω) we prove that the new prime
theorems (691)-(740) 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

[19] **viXra:1009.0044 [pdf]**
*submitted on 11 Sep 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. In this paper using Jiang function J_{2}(ω) we prove that the new prime
theorems (641)-(690) 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

[18] **viXra:1009.0041 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 4 pages

Factoring of the Smarandache Square Product Sequence

**Category:** Number Theory

[17] **viXra:1009.0040 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 6 pages

Factoring of the Smarandache Prime Product Sequence

**Category:** Number Theory

[16] **viXra:1009.0039 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 4 pages

Factoring of the Smarandache Mirror Sequence

**Category:** Number Theory

[15] **viXra:1009.0038 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 3 pages

Factoring of the Smarandache Factorial Product Sequence

**Category:** Number Theory

[14] **viXra:1009.0037 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 5 pages

Factoring of the Smarandache Back Concatenated Cube Sequence

**Category:** Number Theory

[13] **viXra:1009.0036 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 6 pages

Factoring of the Smarandache Back Concatenated Even Sequence

**Category:** Number Theory

[12] **viXra:1009.0035 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 6 pages

Factoring of the Smarandache Back Concatenated Odd Sequence

**Category:** Number Theory

[11] **viXra:1009.0034 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 5 pages

Factoring of the Smarandache Back Concatenated Prime Sequence

**Category:** Number Theory

[10] **viXra:1009.0033 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 5 pages

Factoring of the Smarandache Back Concatenated Square Sequence

**Category:** Number Theory

[9] **viXra:1009.0032 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 4 pages

Factoring of the Smarandache Concatenated Cubic Sequence

**Category:** Number Theory

[8] **viXra:1009.0031 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 6 pages

Factoring of the Smarandache Concatenated Even Sequence

**Category:** Number Theory

[7] **viXra:1009.0030 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 5 pages

Factoring of the Smarandache Concatenated Odd Sequence

**Category:** Number Theory

[6] **viXra:1009.0029 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 4 pages

Factoring of the Smarandache Concatenated Prime Sequence

**Category:** Number Theory

[5] **viXra:1009.0028 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 4 pages

Factoring of the Smarandache Concatenated Square Sequence

**Category:** Number Theory

[4] **viXra:1009.0027 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 4 pages

Factoring of the Smarandache Cubic Product Sequence

**Category:** Number Theory

[3] **viXra:1009.0026 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Micha Fleuren

**Comments:** 10 pages

Factoring of the Smarandache Deconstructive Sequence

**Category:** Number Theory

[2] **viXra:1009.0021 [pdf]**
*submitted on 7 Sep 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 70 pages

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 J_{2}(ω) we prove that the new prime
theorems (591)-(640) 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

[1] **viXra:1009.0004 [pdf]**
*submitted on 2 Sep 2010*

**Authors:** Kunikazu Tanaka

**Comments:**
21 pages

Showing how to derive new
expressions of generating prime
numbers to demonstrate the
Goldbach's Conjecture

**Category:** Number Theory