Advanced Mathematical Formulas to Calculate Prime Numbers

Ameha Tefera Tessema

doi:doi:10.11648/j.mcs.20210606.12

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Advanced Mathematical Formulas to Calculate Prime Numbers

Ameha Tefera Tessema

Published in Mathematics and Computer Science (Volume 6, Issue 6)

Received: 4 March 2021 Accepted: 3 November 2021 Published: 10 November 2021

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Abstract

Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially in the field of information technology, i.e., in data security algorithms. It is easy to generate the product of two prime numbers but extremely difficult and a laborious to decompose prime factors combined together. The RSA system in cryptography uses prime numbers widely to calculate the public and the private keys. Diffie-Hellman Key Exchange in cryptography uses prime numbers in a similar way and in computing hash codes also we use Prime numbers. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. Their appearance within the infinite string of numbers in random fasion that devising a functional equation to correctly predict them, infinitely, has been belived by many mathematician as impossible task. The problem to calculate prime number using a formula posed for long periods. Though different formulae to calculate prime number were developed by Euler, Fermat and mersenne, the formulae work for limited natural numbers and calculate limited prime numbers. However, on this paper the author wants to show how prime number calculated for all values of integers(x).

Published in	Mathematics and Computer Science (Volume 6, Issue 6)
DOI	10.11648/j.mcs.20210606.12
Page(s)	88-91
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Prime Numbers, Prime Numbers Formula, Prime Number Forecasting, Prime Number Distribution, Prime Number Calculation

References

[1]	Apostol, Thomas M., 1976, Introduction to Analytic Number Theory, New York, Springer.
[2]	David Wells, 2005, Prime Numbers: The Most Mysterious Figures in Math. Wiley.
[3]	E. Mabrouk, J. C. H-Castro, M. Fukushima, 2011, Prime number generation using memetic programming, Life Robotics, vol. 16, pp. 53-56.
[4]	Heath, T., 1956, The Thirteen Books of the Elements. Vol. 2, Books 3–9, Dover Publ., New York, 2nd ed.
[5]	Hardy, G. H. and Wright, E. M., 1979, An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 18 and 22.
[6]	J. Barkley Rosser and Lowell Schoenfeld, 1962, Approximate formulas for some functions of prime numbers. Illinois J. Math. Volume 6, Issue 1.
[7]	Matiyasevich, Yuri V., 1999, Formulas for Prime Numbers, in Tabachnikov, Serge (ed.), Kvant Selecta: Algebra and Analysis, II, American Mathematical Society, pp. 13–24.
[8]	Mollin, R. A. and Williams, H. C., 1990, Class Number Problems for Real Quadratic Fields. Number Theory and Cryptology; LMS Lecture Notes Series 154.
[9]	Morris Kline, 1968, Mathematics in modern world, W. h. freeman and co., Sanfrancisco.
[10]	Nagell, T., 1951, Primes in Special Arithmetical Progressions. P 65, New York, Wiley.
[11]	Paul T. B. and Harold G. D., 1996, A Hundred years of prime numbers, The American Mathematical Monthely, Vol. 103, No. 9, PP. 729-741.
[12]	Rowland, Eric S., 2008, A Natural Prime-Generating Recurrence, Journal of Integer Sequences 11: 08.2.8, arXiv: 0710.3217, Bibcode: 2008JIntS..11...28R.
[13]	Samir, B. B, Zardari, M. A and Rezk, Y. A. Y, 2013, Generation of Prime Numbers From Advanced Sequence and Decomposition Mtheod, International Journal of Pure and Applied Mathematics, Vol. 85, No. 5.
[14]	Tenenbaum, G. and M. M. France, 2000, The prime numbers and their distribution. Providence, American Mathematical Society. RI.
[15]	Tejash Desai, 2015, Application of Prime Numbers in Computer Science and the Algorithms Used To Test the Primality of a Number, international Journal of Science and Research, Vol. 4, Issue 9.
[16]	V. S. Igumnov, 2004, Generation of the large random prime numbers. Tomsk State University Russia. Electron Devices and Materials., pp. 117- 118.

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APA Style

Ameha Tefera Tessema. (2021). Advanced Mathematical Formulas to Calculate Prime Numbers. Mathematics and Computer Science, 6(6), 88-91. https://doi.org/10.11648/j.mcs.20210606.12

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ACS Style

Ameha Tefera Tessema. Advanced Mathematical Formulas to Calculate Prime Numbers. Math. Comput. Sci. 2021, 6(6), 88-91. doi: 10.11648/j.mcs.20210606.12

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AMA Style

Ameha Tefera Tessema. Advanced Mathematical Formulas to Calculate Prime Numbers. Math Comput Sci. 2021;6(6):88-91. doi: 10.11648/j.mcs.20210606.12

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@article{10.11648/j.mcs.20210606.12,
  author = {Ameha Tefera Tessema},
  title = {Advanced Mathematical Formulas to Calculate Prime Numbers},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {6},
  pages = {88-91},
  doi = {10.11648/j.mcs.20210606.12},
  url = {https://doi.org/10.11648/j.mcs.20210606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210606.12},
  abstract = {Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially in the field of information technology, i.e., in data security algorithms. It is easy to generate the product of two prime numbers but extremely difficult and a laborious to decompose prime factors combined together. The RSA system in cryptography uses prime numbers widely to calculate the public and the private keys. Diffie-Hellman Key Exchange in cryptography uses prime numbers in a similar way and in computing hash codes also we use Prime numbers. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. Their appearance within the infinite string of numbers in random fasion that devising a functional equation to correctly predict them, infinitely, has been belived by many mathematician as impossible task. The problem to calculate prime number using a formula posed for long periods. Though different formulae to calculate prime number were developed by Euler, Fermat and mersenne, the formulae work for limited natural numbers and calculate limited prime numbers. However, on this paper the author wants to show how prime number calculated for all values of integers(x).},
 year = {2021}
}

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TY  - JOUR
T1  - Advanced Mathematical Formulas to Calculate Prime Numbers
AU  - Ameha Tefera Tessema
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N1  - https://doi.org/10.11648/j.mcs.20210606.12
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AB  - Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially in the field of information technology, i.e., in data security algorithms. It is easy to generate the product of two prime numbers but extremely difficult and a laborious to decompose prime factors combined together. The RSA system in cryptography uses prime numbers widely to calculate the public and the private keys. Diffie-Hellman Key Exchange in cryptography uses prime numbers in a similar way and in computing hash codes also we use Prime numbers. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. Their appearance within the infinite string of numbers in random fasion that devising a functional equation to correctly predict them, infinitely, has been belived by many mathematician as impossible task. The problem to calculate prime number using a formula posed for long periods. Though different formulae to calculate prime number were developed by Euler, Fermat and mersenne, the formulae work for limited natural numbers and calculate limited prime numbers. However, on this paper the author wants to show how prime number calculated for all values of integers(x).
VL  - 6
IS  - 6
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Author Information

Ameha Tefera Tessema

Strategic Planning, Commercial Bank of Ethiopia, Addis Ababa, Ethiopia

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Plain Text BibTeX RIS

APA Style

Ameha Tefera Tessema. (2021). Advanced Mathematical Formulas to Calculate Prime Numbers. Mathematics and Computer Science, 6(6), 88-91. https://doi.org/10.11648/j.mcs.20210606.12

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ACS Style

Ameha Tefera Tessema. Advanced Mathematical Formulas to Calculate Prime Numbers. Math. Comput. Sci. 2021, 6(6), 88-91. doi: 10.11648/j.mcs.20210606.12

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AMA Style

Ameha Tefera Tessema. Advanced Mathematical Formulas to Calculate Prime Numbers. Math Comput Sci. 2021;6(6):88-91. doi: 10.11648/j.mcs.20210606.12

Copy | Download

@article{10.11648/j.mcs.20210606.12,
  author = {Ameha Tefera Tessema},
  title = {Advanced Mathematical Formulas to Calculate Prime Numbers},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {6},
  pages = {88-91},
  doi = {10.11648/j.mcs.20210606.12},
  url = {https://doi.org/10.11648/j.mcs.20210606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210606.12},
  abstract = {Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially in the field of information technology, i.e., in data security algorithms. It is easy to generate the product of two prime numbers but extremely difficult and a laborious to decompose prime factors combined together. The RSA system in cryptography uses prime numbers widely to calculate the public and the private keys. Diffie-Hellman Key Exchange in cryptography uses prime numbers in a similar way and in computing hash codes also we use Prime numbers. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. Their appearance within the infinite string of numbers in random fasion that devising a functional equation to correctly predict them, infinitely, has been belived by many mathematician as impossible task. The problem to calculate prime number using a formula posed for long periods. Though different formulae to calculate prime number were developed by Euler, Fermat and mersenne, the formulae work for limited natural numbers and calculate limited prime numbers. However, on this paper the author wants to show how prime number calculated for all values of integers(x).},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Advanced Mathematical Formulas to Calculate Prime Numbers
AU  - Ameha Tefera Tessema
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210606.12
DO  - 10.11648/j.mcs.20210606.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 88
EP  - 91
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210606.12
AB  - Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially in the field of information technology, i.e., in data security algorithms. It is easy to generate the product of two prime numbers but extremely difficult and a laborious to decompose prime factors combined together. The RSA system in cryptography uses prime numbers widely to calculate the public and the private keys. Diffie-Hellman Key Exchange in cryptography uses prime numbers in a similar way and in computing hash codes also we use Prime numbers. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. Their appearance within the infinite string of numbers in random fasion that devising a functional equation to correctly predict them, infinitely, has been belived by many mathematician as impossible task. The problem to calculate prime number using a formula posed for long periods. Though different formulae to calculate prime number were developed by Euler, Fermat and mersenne, the formulae work for limited natural numbers and calculate limited prime numbers. However, on this paper the author wants to show how prime number calculated for all values of integers(x).
VL  - 6
IS  - 6
ER  -

Copy | Download