Jabari Zakiya - Academia.edu (original) (raw)

Videos by Jabari Zakiya

This video describes my proof of the Twin Prime and Polignac's conjectures, showing there are an ... more This video describes my proof of the Twin Prime and Polignac's conjectures, showing there are an infinite number of prime pairs differing by any even value n. It uses Prime Generator Theory (PGT) to develop the mathematical framework of Prime Generator (PGs), which are comprised of residues which generate the primes. Each PG has a fundamental Prime Generator Sequence (PGS), which is their characteristic gap spacing between the residues, which have a mirror image symmetry distribution. As each PGs modulus becomes larger, they contain an always increasing number of residues gaps, old ones from smaller PGs, and new larger ones as the primes get farther apart on average, but form in clusters of primes in close proximity. It's meant to be accessible to people without a formal background in math, and uses a plethora of pictures, diagrams, and graphs to show and explain the math in a user friendly manner. It's a companion to my paper - On The Infinity of Twin Primes and other K-tuples.

11 views

Papers by Jabari Zakiya

Journal of humanities & social sciences, Mar 1, 2024

Presented is a summary and outline of my formal proof of the Twin Primes and Polignacs Conjecture... more Presented is a summary and outline of my formal proof of the Twin Primes and Polignacs Conjectures, to provide the general conceptual and logical structure of the paper's mathematical foundations.

The Hardy-Littlewood twin prime constant is a metric to compute the distribution of twin primes. ... more The Hardy-Littlewood twin prime constant is a metric to compute the distribution of twin primes. Using Prime Generator Theory (PGT) it is shown it is more easily mathematically and conceptually derived, and the correct value is a factor of 2 larger.

FICA withholding from wages is currently used to fund Social Security. It uses a Cap with no Floo... more FICA withholding from wages is currently used to fund Social Security. It uses a Cap with no Floor system, which subjects the first dollar of wage earners salaries to FICA, up to a wage cap, after which FICA is no longer applied. What is shown here, is that a Floor with no Cap system is better, for the myriad of reasons provided herein, and should be adopted by Congress to replace the current system.

viXra, Jun 1, 2020

This paper describes the mathematical foundation of Prime Generators and their use in creating a ... more This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypothesis.

Journal of Current Trends in Computer Science Research, 2023

The paper explains and describes in great detail, a novel simple|fast new method, based on Prime ... more The paper explains and describes in great detail, a novel simple|fast new method, based on Prime Generator Theory (PGT), to find, count, and numerate the number of Twin and Cousin Primes within a range of 64-bit numbers, which can be modified to find other prime k-tuples. Coded implementations in 6 software languages are provided, with performance data.

Primorials in Pi, 2023

I show, using Prime Generator Theory, hidden in the Euler Zeta function for the positive even int... more I show, using Prime Generator Theory, hidden in the Euler Zeta function for the positive even integer values of s, is the means to derive an exquisite and elegant formula for representing and calculating Pi (to arbitrary accuracy) which has heretofore been missed (for centuries). I provide a software implementation of the algorithm to compute the digits of Pi, with a table of results showing rates of converges in terms of primes. The methods presented here may be able to be applied to obtain a better conceptual understanding, and numerical forms, for the odd integer values of s as well.

In 2014 I released The Segmented Sieve of Zakiya (SSoZ) [1]. It described a general method to fin... more In 2014 I released The Segmented Sieve of Zakiya (SSoZ) [1]. It described a general method to find primes using an efficient prime sieve based on Prime Generators (PG). I expanded upon it, and in 2018 I released The Use of Prime Generators to Implement Fast Twin Primes Sieve of Zakiya (SoZ), Applications to Number Theory, and Implications for the Riemann Hypotheses [2]. The algorithm has been improved and now also used to find Cousin Primes. This paper explains in detail the what, why, and how of the algorithm and shows its implementation in 6 software languages, and performance data for these 6 languages run on 2 different cpu systems, with 8 and 16 threads.

As an aide to help focus people's understanding of my paper - On The Infinity of Twin Primes and ... more As an aide to help focus people's understanding of my paper - On The Infinity of Twin Primes and other K-tuples - I've created this Companion Test Quiz. The answers to the questions come directly from the content in the paper. If you can answer these (fairly easy) questions then you have a good grasp of the paper. You can email me any questions, and your answers, and I’ll send you the answer sheet.

viXra, 2020

This paper describes the mathematical foundation of Prime Generators and their use in creating a ... more This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypothesis.

viXra, 2024

The paper uses the structure and math of Prime Generators to show there are an infinity of twin p... more The paper uses the structure and math of Prime Generators to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.

The present invention describes methods and systems to perform hash algorithms as logic gate func... more The present invention describes methods and systems to perform hash algorithms as logic gate functions. It processes an N-bit block of data into the M-bit has or message digest of the block in one (1) process cycle instead of the multiple cycles generally
required. The minimum process time is the total propagation delay of an input black through the core logic for an implementing technology. A message requiring Y blocks to process would require no more than Y process (clock) cycles to produce the final hash
value. This creates very simple and fast implementations of hash algorithms which enable them to be simply and easily integrated into any system.

Systems And Methods For Implementing Encryption Algorithms, Dec 13, 2001

Patent application describing method to completely implement encryption algorithms as non-sequent... more Patent application describing method to completely implement encryption algorithms as non-sequential hardware devices.

The paper uses Prime Generators to create progressively faster integer primality tests in Ruby. T... more The paper uses Prime Generators to create progressively faster integer primality tests in Ruby. The Ruby standard library file prime.rb contains the class Integer methods prime? and prime_division (for factorization). I present here simpler and significantly faster methods as replacements.

The paper uses the structure and math of Prime Generators to show there are an infinity of twin p... more The paper uses the structure and math of Prime Generators to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.

This paper describes the mathematical foundation of Prime Generators and their use in creating a ... more This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypotheses

The paper presents a simple and fair method to proportionally allocate presidential electors from... more The paper presents a simple and fair method to proportionally allocate presidential electors from each state, in a transparent and reproducible manner, based solely on mathematical considerations. States are free to adopt this method for allocating their electors on their own, and citizen led movements can organize to create ballot initiatives for its adoption in their states to force it. Its adoption will create a host of benefits to voters and the country, resulting in more fair and democratic electoral outcomes.

primes-utils is a Rubygem which provides a suite of utility methods to list|count primes over ran... more primes-utils is a Rubygem which provides a suite of utility methods to list|count primes over ranges, factoring, finding the nth prime, and primality testing. This handbook explains the use of Prime Generators, which are used as the mathematical foundation for most of the methods, and provides the Ruby source code for the gem.

This paper describes an efficient and fast method to implement a Segmented Sieve of Zakiya (SSoZ)... more This paper describes an efficient and fast method to implement a Segmented Sieve of Zakiya (SSoZ). Its structure is based on two key design concepts: 1) a segment is a byte array consisting of B integral bytes of KB residues groups for a given Prime Generator (pg), and 2) the bits in each byte represent the residues (tracks) for the pg, and are processed the same within each byte. This structure creates very simple components that can be efficiently coded, that scale to any size prime generator for any size cpu that provides byte addressable memory. This allows the SSoZ to be memory independent of cpu size.

The SSoZ extends the Sieve of Zakiya (SoZ) to allow it to process very large numbers with a small memory footprint. It is also inherently realizable by parallel processing, utilizing multicore processors. This will allow the SSoZ to actualize the theoretically possible performance gains by using larger size Strictly Prime (SP) Generators

This video describes my proof of the Twin Prime and Polignac's conjectures, showing there are an ... more This video describes my proof of the Twin Prime and Polignac's conjectures, showing there are an infinite number of prime pairs differing by any even value n. It uses Prime Generator Theory (PGT) to develop the mathematical framework of Prime Generator (PGs), which are comprised of residues which generate the primes. Each PG has a fundamental Prime Generator Sequence (PGS), which is their characteristic gap spacing between the residues, which have a mirror image symmetry distribution. As each PGs modulus becomes larger, they contain an always increasing number of residues gaps, old ones from smaller PGs, and new larger ones as the primes get farther apart on average, but form in clusters of primes in close proximity. It's meant to be accessible to people without a formal background in math, and uses a plethora of pictures, diagrams, and graphs to show and explain the math in a user friendly manner. It's a companion to my paper - On The Infinity of Twin Primes and other K-tuples.

11 views

Journal of humanities & social sciences, Mar 1, 2024

Presented is a summary and outline of my formal proof of the Twin Primes and Polignacs Conjecture... more Presented is a summary and outline of my formal proof of the Twin Primes and Polignacs Conjectures, to provide the general conceptual and logical structure of the paper's mathematical foundations.

The Hardy-Littlewood twin prime constant is a metric to compute the distribution of twin primes. ... more The Hardy-Littlewood twin prime constant is a metric to compute the distribution of twin primes. Using Prime Generator Theory (PGT) it is shown it is more easily mathematically and conceptually derived, and the correct value is a factor of 2 larger.

FICA withholding from wages is currently used to fund Social Security. It uses a Cap with no Floo... more FICA withholding from wages is currently used to fund Social Security. It uses a Cap with no Floor system, which subjects the first dollar of wage earners salaries to FICA, up to a wage cap, after which FICA is no longer applied. What is shown here, is that a Floor with no Cap system is better, for the myriad of reasons provided herein, and should be adopted by Congress to replace the current system.

viXra, Jun 1, 2020

This paper describes the mathematical foundation of Prime Generators and their use in creating a ... more This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypothesis.

Journal of Current Trends in Computer Science Research, 2023

The paper explains and describes in great detail, a novel simple|fast new method, based on Prime ... more The paper explains and describes in great detail, a novel simple|fast new method, based on Prime Generator Theory (PGT), to find, count, and numerate the number of Twin and Cousin Primes within a range of 64-bit numbers, which can be modified to find other prime k-tuples. Coded implementations in 6 software languages are provided, with performance data.

Primorials in Pi, 2023

I show, using Prime Generator Theory, hidden in the Euler Zeta function for the positive even int... more I show, using Prime Generator Theory, hidden in the Euler Zeta function for the positive even integer values of s, is the means to derive an exquisite and elegant formula for representing and calculating Pi (to arbitrary accuracy) which has heretofore been missed (for centuries). I provide a software implementation of the algorithm to compute the digits of Pi, with a table of results showing rates of converges in terms of primes. The methods presented here may be able to be applied to obtain a better conceptual understanding, and numerical forms, for the odd integer values of s as well.

In 2014 I released The Segmented Sieve of Zakiya (SSoZ) [1]. It described a general method to fin... more In 2014 I released The Segmented Sieve of Zakiya (SSoZ) [1]. It described a general method to find primes using an efficient prime sieve based on Prime Generators (PG). I expanded upon it, and in 2018 I released The Use of Prime Generators to Implement Fast Twin Primes Sieve of Zakiya (SoZ), Applications to Number Theory, and Implications for the Riemann Hypotheses [2]. The algorithm has been improved and now also used to find Cousin Primes. This paper explains in detail the what, why, and how of the algorithm and shows its implementation in 6 software languages, and performance data for these 6 languages run on 2 different cpu systems, with 8 and 16 threads.

As an aide to help focus people's understanding of my paper - On The Infinity of Twin Primes and ... more As an aide to help focus people's understanding of my paper - On The Infinity of Twin Primes and other K-tuples - I've created this Companion Test Quiz. The answers to the questions come directly from the content in the paper. If you can answer these (fairly easy) questions then you have a good grasp of the paper. You can email me any questions, and your answers, and I’ll send you the answer sheet.

viXra, 2020

This paper describes the mathematical foundation of Prime Generators and their use in creating a ... more This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypothesis.

viXra, 2024

The paper uses the structure and math of Prime Generators to show there are an infinity of twin p... more The paper uses the structure and math of Prime Generators to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.

The present invention describes methods and systems to perform hash algorithms as logic gate func... more The present invention describes methods and systems to perform hash algorithms as logic gate functions. It processes an N-bit block of data into the M-bit has or message digest of the block in one (1) process cycle instead of the multiple cycles generally
required. The minimum process time is the total propagation delay of an input black through the core logic for an implementing technology. A message requiring Y blocks to process would require no more than Y process (clock) cycles to produce the final hash
value. This creates very simple and fast implementations of hash algorithms which enable them to be simply and easily integrated into any system.

Systems And Methods For Implementing Encryption Algorithms, Dec 13, 2001

Patent application describing method to completely implement encryption algorithms as non-sequent... more Patent application describing method to completely implement encryption algorithms as non-sequential hardware devices.

The paper uses Prime Generators to create progressively faster integer primality tests in Ruby. T... more The paper uses Prime Generators to create progressively faster integer primality tests in Ruby. The Ruby standard library file prime.rb contains the class Integer methods prime? and prime_division (for factorization). I present here simpler and significantly faster methods as replacements.

The paper uses the structure and math of Prime Generators to show there are an infinity of twin p... more The paper uses the structure and math of Prime Generators to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.

This paper describes the mathematical foundation of Prime Generators and their use in creating a ... more This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypotheses

The paper presents a simple and fair method to proportionally allocate presidential electors from... more The paper presents a simple and fair method to proportionally allocate presidential electors from each state, in a transparent and reproducible manner, based solely on mathematical considerations. States are free to adopt this method for allocating their electors on their own, and citizen led movements can organize to create ballot initiatives for its adoption in their states to force it. Its adoption will create a host of benefits to voters and the country, resulting in more fair and democratic electoral outcomes.

primes-utils is a Rubygem which provides a suite of utility methods to list|count primes over ran... more primes-utils is a Rubygem which provides a suite of utility methods to list|count primes over ranges, factoring, finding the nth prime, and primality testing. This handbook explains the use of Prime Generators, which are used as the mathematical foundation for most of the methods, and provides the Ruby source code for the gem.

This paper describes an efficient and fast method to implement a Segmented Sieve of Zakiya (SSoZ)... more This paper describes an efficient and fast method to implement a Segmented Sieve of Zakiya (SSoZ). Its structure is based on two key design concepts: 1) a segment is a byte array consisting of B integral bytes of KB residues groups for a given Prime Generator (pg), and 2) the bits in each byte represent the residues (tracks) for the pg, and are processed the same within each byte. This structure creates very simple components that can be efficiently coded, that scale to any size prime generator for any size cpu that provides byte addressable memory. This allows the SSoZ to be memory independent of cpu size.

The SSoZ extends the Sieve of Zakiya (SoZ) to allow it to process very large numbers with a small memory footprint. It is also inherently realizable by parallel processing, utilizing multicore processors. This will allow the SSoZ to actualize the theoretically possible performance gains by using larger size Strictly Prime (SP) Generators

This draft chapter develops the mathematical framework for determining the residue gap structure ... more This draft chapter develops the mathematical framework for determining the residue gap structure of primorial modular groups. I start by showing the data for the residue gaps size tallies, then use it to develop recursive forms to compute the gap coefficient values. I then develop the algebraic structure to compute them for any Pn generator, which results in a table of rational coefficients, which when multiplied by the appropriate reduced primorials, compute the residue gap counts, for any gap size, for any Pn generator

This draft chapter- The Foundations of Prime Generator Theory (PGT) - provides the mathematical, ... more This draft chapter- The Foundations of Prime Generator Theory (PGT) - provides the mathematical, conceptual, and logical foundations of Prime Generator Theory (PGT). It uses easy to understand language, with pictures and graphs, to show how the simple structure of modular groups allows us to easily reveal and characterize the nature and distribution of the primes, and their gaps.

As an aide to help focus people's understanding of my paper: "On The Infinity of Twin Primes and... more As an aide to help focus people's understanding of my paper:

"On The Infinity of Twin Primes and other K-tuples"
https://www.academia.edu/41024027/On_The_Infinity_of_Twin_Primes_and_other_K_tuples

I've created this Companion Test Quiz. The answers to the questions come directly from the content in the paper. If you can answer these (fairly easy) questions then you have a good grasp of the paper. You can email me any questions, and your answers, and I’ll send you the answers sheet.