[14] **viXra:1101.0102 [pdf]**
*submitted on 31 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 18 pages.

D.Zagier (1984) and K.Inkeri(1990) said[7]: Jiang mathematics is true, but Jiang
determinates the irrational numbers to be very difficult for prime exponent p>2. In 1991
Jiang studies the composite exponents n=15,21,33,...,3p and proves Fermat last theorem. In
1986 Gerhard Frey places Fermat last theorem at the elliptic curve that is Frey curve.
Andrew Wiles studies Frey curve. In 1994 Wiles proves Fermat last theorem.
Conclusion:Jiang proof is direct and simple,but Wiles proof is indirect and complex.

**Category:** Number Theory

[13] **viXra:1101.0092 [pdf]**
*replaced on 4 Mar 2011*

**Authors:** Marco Ripà

**Comments:** This paper is 17 pages long and the Italian version has already been published
here: (http://www.rudimathematici.com/bookshelf/bookshelfdb.php).

The paper shows that the only possible prime terms of the "consecutive sequence"
(1,12,123,1234...) represent of the total, and their structure is explicited. This outcome is
then extended to every permutation of their figures. The previous result is applied to a
consistent subset of elements belonging to the circular sequence (resulting from the consecutive
one), identifying moreover the 31 first primes. Therefore, a criterion is illustrated (further
extendible) that progressively reduces the numerousness of the "candidate prime numbers".
Section 3.3 is devoted to the solution of a similar problem. The last section introduces a
new sequence which, although much larger, has the same properties as the previous ones, and
it also proposes a few open problems.

**Category:** Number Theory

[12] **viXra:1101.0091 [pdf]**
*submitted on 28 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 18 pages

1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate
into two biquadrates, or in general any power higher than the second into powers of like degree: I
have discovered a truly marvelous proof, which this margin is too small to contain." (6)

**Category:** Number Theory

[11] **viXra:1101.0090 [pdf]**
*submitted on 28 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 18 pages

1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate
into two biquadrates, or in general any power higher than the second into powers of like degree: I
have discovered a truly marvelous proof, which this margin is too small to contain." (5)

**Category:** Number Theory

[10] **viXra:1101.0089 [pdf]**
*submitted on 28 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 20 pages

1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate
into two biquadrates, or in general any power higher than the second into powers of like degree: I
have discovered a truly marvelous proof, which this margin is too small to contain." (4)

**Category:** Number Theory

[9] **viXra:1101.0087 [pdf]**
*submitted on 26 Jan 2011*

**Authors:** Huping Hu, Maoxin Wu

**Comments:** 6 pages

In this short paper, the authors briefly discuss their preliminary thoughts on the
coding of DNA and the hexagrams of I Ching based on the principle of existence. It is shown
that one may mathematically generate the DNA codes from the principle of existence. It is
further shown that one may also mathematically generate the hexagrams of Chinese I Ching from
the principle of existence.

**Category:** Number Theory

[8] **viXra:1101.0086 [pdf]**
*submitted on 26 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 21 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate
into two biquadrates, or in general any power higher than the second into powers of like degree: I
have discovered a truly marvelous proof, which this margin is too small to contain."

**Category:** Number Theory

[7] **viXra:1101.0071 [pdf]**
*submitted on 22 Jan 2011*

**Authors:** Petru Minut

**Comments:** 4 pages

In 1980, F.SMARANDACHE introduced (see [5]) the function ...

**Category:** Number Theory

[6] **viXra:1101.0070 [pdf]**
*submitted on 22 Jan 2011*

**Authors:** Guo Xiaoyan, Yuan Xia

**Comments:** 147 pages, in Chinese

New Progress on
Smarandache Problems Research

**Category:** Number Theory

[5] **viXra:1101.0051 [pdf]**
*submitted on 16 Jan 2011*

**Authors:** Tong Xin Ping

**Comments:** 3 pages

1-Number Sieve: It is the Eratosthenes'-Number Sieve and the da Silva-Sylvester
formula. 2-Number Sieve: We can obtain result of Goldbach' conjecture and the number of
solutions of Goldbach problem. 3-Number Sieve: We can obtain result p_{3} in N= p_{3}+p_{i} P_{1}
and 3-Inclusion-exclusion formula.

**Category:** Number Theory

[4] **viXra:1101.0047 [pdf]**
*submitted on 14 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 117 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 (1041)-(1090) contain infinitely many prime
solutions and no prime solutions.

**Category:** Number Theory

[3] **viXra:1101.0032 [pdf]**
*submitted on 7 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 122 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 (991)-(1040) contain infinitely many prime
solutions and no prime solutions...

**Category:** Number Theory

[2] **viXra:1101.0028 [pdf]**
*submitted on 6 Jan 2011*

**Authors:** Tim Jones

**Comments:** 5 pages

A geometric proof of the irrationality of π is given. It uses an
evaluation of the area given by the product of two symmetric functions,
together with bounds on the integral. The symmetric functions embed
the assumption of rational π; one function is dependent on n; as the
evaluation of the integral exceeds the upper bound for large n for any
given rational π, a contradiction is obtained. This proof has been
criticized, but here some counters to the criticism are offered.

**Category:** Number Theory

[1] **viXra:1101.0022 [pdf]**
*submitted on 4 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 98 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 (941)-(990) contain infinitely many prime
solutions and no prime solutions.

**Category:** Number Theory