Equations for All the Primes Numbers

with this work the equation is defined for the primes numbers; this one work is based on additive theory number and arithmetical progressiones.


Introduction
In this work the equations are definite and demonstrated for all the prime numbers. I have to say that all my investigation was centred exclusively in the additive theory [1] and, arithmetic progression [2].

Methodology
The investigation has been exhaustive and extended in the time since, the aim, always it was to define an equation for the odd numbers of such form that his possible fectoring, was with the minor possible number of numbers. Obtained aim.
For definition a prime number is any entire number that takes the unit as dividing only ones the same number.
The minor odd number that generates other odd in x(1 + n) is (x = 3), in order that result is always an odd number, (n) has to (2b); with which it stay.
3 + 2b = 2c + 1 If now in this equality we want that all the odd numbers are multiples of three we will have.

+ · 2b = + 6b
And, for other odd not multiple of three, simply we will add an even number, that is to say.
If we have avoided the multiple of five and seven, the following thing that we will do will be to demonstrate that it is not possible to have numbers that could be a factor. For it we indicate the equations (3) and (4) into arithmetic progressions [2]; it is to say. In these progressions we have numbers that are factor, this happens when (a) is equal or the multiple one of the odd respective number. To avoid these mistakes, we add in the denominators of the equations ( 3) and (4 ) the respective odd ones of the arithmetic progressions. Therefore 5 + 6[5a + (1; 2; 3; 4)] (5; 7; 11; 17; 23; 29) ̸ = Z

Discussion
We were observing that in the denominator of the second equation previous it appears the number three, this owes to that. If is possible to have in the root of the equation (5) or (6) and odd number that is multiple of a number different from the indicated ones in the denominatot. I demonstrate that the only odd number is the number three, with the following equation.
(2c + 1)(2b + 1) = 42a + (13; 19; 25; 31; 37; 43; 49) 4cb + 2c + 2b = 42a + (12; 18; 24; 30; 36; 42; 48) I demonstrate that does not exist any number, product of two odd ones for the equation (5) with the exception of his denominators, and in turn that the equation (6) admits as value the number three. Therefore having in the denominator of the equation (6) the number three we rejected as possible mistake to say, that the numbers that define the equations do not be a prime number.

Therefore any entire number that does not belong to the equation (5) or (6) is of absolute form a prime number.
Later we define the equation for the twins prime numbers. It is to say that if we take the values of the numerator in the equations (3) and (4)  And therefore: [7a + (1; 2; 3; 4; 5; 6)] = [5a ′ + (1; 2; 3; 4)] with these equalities we will define the equation to know the twins prime numbers directly, since: All these equalities diminish to the following ones: Therefore the equation for any twin prime number is in the following form, with (p > 7); (a = 0 → ∞)

Conclusion
With this article we have solved the four problems that Edmun Landau mentioned unattackable at the present state of science in the mathematicians' fifth International Congress (1912).
-Golbach Conjecture: the sum of two prime numbers, majors that two is always an even number.

Introduction
In the equation (5) and (6)  The motive of this change is to avoid certain mistakes thet originate when a prime numbers multiples (whose origin is in one of the equations) for one of the numbers of the denominator of other one. Example. In the equation for the prime numbers the sign (±) is replaced by the sign (+). I turn I refer to the value that will have always (7a ′ + (1; 2; 3; 4)); this value will by exclusively the one that fulfills the equality [(7a ′ + (1; 2; 3; 4) = 5a + (1; 2; 3; 4)] [7 + 6[7a ′ + (1; 2; 3; 4)] − 2 ̸ = 5n Within this annexe we have demonstrated absolutely the crux of the prime numbers.

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Equations for All the Primes Numbers

Main Results
The error is in the product between the two equations. There are values for (30a + (11; 17; 23; 29)) that are not multiples of any of the numbers of the denominator and we would say that are prime (false). The error originated in a single value for the group of seven; specifically (7 + 6[7b + (1; 2; 3; 4; 5; 6)]) with (b = 3).

Demonstration
Throughout the product between the two equations always we have a value . The only term that is not a multiple of six is always the product of two integers (conductores), (p = (11; 17; 23; 29)) and p 1 = (13; 19; 31; 37; 43). If now we subtract the value of (11; 17; 23; 29) is become multiples of six and we can divide both terms.

Recent Errors in the Equations of Andri Lopez
They are in the product of prime numbers of the seven gtoup and in the power of prime numbers.
(i) The last error we have is in the product two primes of the group seven; is solved with the following equations. The distribution of prime numbers is always in every interval. between: (30a + 11) and (42a + 43). The number of primes per interval ranges from a minimum of two and a maximum of seven.