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The Euler Riemann Zeta Function

Is a function that uses real numbers, continuously, to calculate spaces in the space-time. This spaces can be the prime numbers.

While with Life primes, also uses real numbers, to go from one previous prime point n, to another prime, in the space-time.

Sep 18, 2018



Welcome to the number 2 of Mutants magazine.
10 Short articles for free thinkers.

Special Edition: Life Primes
A new vision that explains prime numbers, building blocks of maths, and a practical way to calculate them.

Sep 16, 2018.


1. Life Primes 

Life Primes is the structured, ordered, deterministic, series of the prime numbers. 
                        Prime( previous n )= Prime( current ) / L 

Every prime (p), is the result of multiplying a previous prime n, by the series value L.  
I named it L, as Life.  L is a real number that is not a natural number.

There is no need of input two primes to get the position of next prime n.
One prime generates the succession in the series: 
                 Prime(previous n) = Prime(current) / L

clear the equation: 
                 Prime(current) = Prime(previous n)  x  L

To get the previous prime:  divide the current prime by L,
To get the current prime:    multiply the previous prime n by L,
To get the successor prime, if there were one: multiply the current prime by L

Life Primes is the prime series, ordered, determinated, successive, of prime numbers, where:    
                                  Prime(current) =  Prime(previous n)  x  L

Alberto Curiel, September 16, 2018


2. Primes series are succesive & determined

Prime  numbers are determined series,  successive, ordered by it predecesor n, where:
                     Prime(current) =  Prime(previous n)  multiplied by  L 

For  example:
Prime 149,975,123 , has 42 sucessive predecessors/sucessors, where:
                                  Prime(previous n) = Prime(current)  /  L
I define with the letters L,  or  ש  , the value result from the series of prime numbers.

Alberto Curiel, Septiembre 16, 2018


3. Primes are deterministics

In the Prime Series, the current prime is the result of the unavoidable consequence of the previous prime n, multiplied by the value L 

Primes have its determined values from the previous prime n.
With full certainty that the previous prime in the prime series are primes, as the formula is:
                    current prime = Prime(previous n)  multiplied by  L
                       f(p) = f(p n)  x  L

Primes are deterministics. 

Alberto Curiel, September 16, 2018


4. Primes space

In the Prime series Formula:
                       Prime(current)  = Prime(previous n)  x  L

Prime(previous) x L  points to the space where primes are located:
                           prime(previous n) multiplied by L.

For example:
In the prime 149,975,123  there is a prime number in the value Prime x L, in its 42 consecutive predecessors.  Curious note: this example of 42 primes, is almost the double of the largest known series in primes. 

The space of the prime series, & path to move in the primes is:
          Prime(current) = Prime(previous n) multiplied by L
Alberto Curiel, September 16, 2018


5. Life Primes Algorithm o(1)

Formula:         Current Prime = Prime(previous n) multiplied  by L

The value of the prime is known in one operation o(1), as the current prime is set by the previous prime(n) multiplied by L.  
If there is a successive prime, its value and location is set by the current prime multiplied by L. 

Prime numbers are optimized in its distribution, and for large primes:  One operation to calculate the previous, current, or successor prime.

Example of operations:
For a prime with value higher than 100,000,000: (one hundred millions) :  
1 if the previous prime (n) is known,  or between 2 to 43  if you want to travel all the path

For a prime with value higher than 1, 000,000, 000,000, 000,000: ( 1 quintillion) :
1 if the prime(previous n) is known. Or between 2 and 100 if you want to travel the all path -estimated-

For 100 Millions digits long primes, 1 billion digits long primes, and successive (the longest prime numbers known in the future):
1 if the prime( previous n) is known. Or between 2 operations to tens of millions, if you want to travel all the path -estimated-

Previous prime with L location path, allows to know its successive, current or predecessor prime, each one in one operation: 
                            Next  prime n = current prime multiplied by L

Alberto Curiel, September 16, 2018


6. Primes, Series and Fibonacci

Geometrically, this known series represent a limit when growth. For example, at the origin of the Fibonacci series, the relation in the angles express the growth,the transition from a figure with area equal to one, to a figure with area equal to two, rotated in space-time.

Phi in a pentagon, is relation among sides of a pentagon figure, and represents growth too, for example.

Regarding to the origin of the numbers, there are three options considered:

1) in its origin, the numbers originated at different time. To exist the number 2 (the duality) there must first exist the number 1 (the unity), or

2) in its origin, the numbers originated at the same time. The number 3 (multiplicity) appeared simultaneously with the number 2 (the duality) and the number 1 (the unity).

3)in its origin, prime numbers are the origin of numbers. Non prime numbers (like even numbers) are like chords, the resonating waves of prime numbers.

In all cases, if the primes appeared simultaneously, successively, or first, the prime series sets the succession, relation, and path among a determined prime and its successive prime n, in space-time, using in one input prime.

Prime series geometric figure starts from the circle. All primes and its precessor prime n, are in its own auto-ordered space and path:
                                 current Prime  = Prime(previous n) multiplied by L
                                  f(p) = f(previous n) x L

Alberto Curiel, September 16, 2018


7. Time displacement: Primes

                                 Current Prime = Prime(previous n)  x  L

The current prime is determinated by the value of the previous prime multiplied by L
The formula points backwards in time, where each prime starts from a previous prime n

Life Primes series, seeing as succession in time, defines that to exist the current prime, the previous prime n, must exists or have existed before, previously in time.  If we are in a sucessor prime, the predecessor prime existed.

Life Primes series, seeing as simultaneous existence of primes, gives the linked path among all the primes (predecessors, current, successors) in time and space.

Alberto Curiel, September 16, 2018


8. Primes, a nature's blockchain

Series are successions of values.
Blockchain is a linked series, linked in time, and the current value and time is added.
Geometric series like Fibonacci, phi include the value or relation of the previous segment, using 2 values. 
Primes series is primes linked, using the value of the previous prime values, in an auto-optimized space and path:
                                 current prime = ( previous prime n ) x L

Nature shows  how is a linked prime series. 

Alberto Curiel, September 16, 2018


9. Three of primes

An example to explain L

At the center of the garden of the numbers, there is a tree of knowledge of the prime numbers, to which the prime numbers are united. L is like this continuous tree. Only the prime numbers have the property of being united, constituted, and nourished from the tree: 
                        current prime = (previous prime) x L 

The shape of the tree:  At the base of the tree, is the tree trunk. A tree trunk gives structure and strength, it is a continuous unity, it unites all the tree simultaneously: Without trunk there is no tree. The tree has an initial prime in the base. When you look up the tree, the number of branches increases, as the number of primes increases.
The tree trunk and its branches are thick, and change, as the amount of primes changes. Look a little higher in the tree. You are advancing in the succession, travelling the tree. Sometimes there are new more branches, looks more dense are there are new more primes. The branches point in different directions, sometimes the branches almost join. The quantity of new primes changes, as there can be new or less new branches in that part of the tree.  
Primes are distributed in unique way: all are attached to the tree.

The coordinate of each prime in the tree is its value. To move forward, or backward, from one prime to another, you move over the branch easily, because the value of each prime is based in the previous (prime n) by the three branch value: L , in the series. You travel around all the primes tree safely, moving forward in the branches (next prime n) or backwards (previous prime n), simply by:
                             current prime = (previous prime n) multiplied by L

Travelling in the tree, is moving in the tree of primes.  Look up the tree, the tree branches are longer, thin, spaced, and everytime there are less new primes. It is changing. If you look to the top of the tree, the number of new primes is decreasing, while the L tree grows towards the limit, the infinite sky.

Alberto Curiel, September 16, 2018


10. An extension to the prime numbers

Time ago, the imaginary numbers were defined as an extension to complement and facilitate the use in operations with real numbers, like example, to facilite the root of -1

Life prime series, is based in the previous prime, which is an integer:
                     Current prime = (Previous prime n) x L 

In the series, the aditional complement to the prime numbers is L, which is also the factor of time and space, givinig the unique position of the prime in the prime number series.  

Life Primes are prime series, determinated, ordered, with only succession of predecessor, current, and successor primes n, located in time and space with L, continuous value for primes. Facilitating operations & extending the panarama of primes.

Alberto Curiel, September 16, 2018


Mutants Magazine

Welcome to the Mutant First Magazine.
Short articles for Free thinkers.

Sep 9, 2018.


Large prime numbers

While working on the Flower of Life, I found a fast way to calculate 100 million digits prime numbers numbers and inclusive 1,000 million digit prime number.

This new formula worked easily for prime numbers at 2
to the power 34. Computers have the 64 bit limitation,

To verify a 100 million prime digit number on a simple computer, solving the 64 bit limitation. I am developing the tools to store and evaluate this long prime numbers easily. It have to be practical to use. 

The use of large prime numbers increase safety of communications, wallets, data in Mutants, and the tools developed will reinforce the environment of flower of Life AI.

by A.C. 2018


Predictable PI

Traditionally is believed that Pi decimals are kind of random.

But what if the digits in PI were predictable? if there were a constant value in Pi?  

While working on the Flower of Life environment, I found that there is a way where PI shows predictable.

I am using this Pi property for enhancing Mutants Flower of Life environment.

by A.C. 2018

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