### Abstract

The properties of the function 2ab+a+b in the domain of natural numbers are introduced, analyzed, and exhibited to illustrate how these single out all the prime numbers from the full set of odd numbers in contrast that, it is generally said that primes show quite "erratic" distribution. The characterization of odd primes vs. odd non-primes can be done with it among the odd natural numbers as an analogue to the other, well known type of fundamental characterization for irrational and rational numbers among the real numbers. The prime number theorem, twin primes and erratic nature of primes, are also commented upon with respect to selection.

Original language | English |
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Title of host publication | International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016 |

Publisher | American Institute of Physics Inc. |

Volume | 1863 |

ISBN (Electronic) | 9780735415386 |

DOIs | |

Publication status | Published - Jul 21 2017 |

Event | International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 - Rhodes, Greece Duration: Sep 19 2016 → Sep 25 2016 |

### Other

Other | International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 |
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Country | Greece |

City | Rhodes |

Period | 9/19/16 → 9/25/16 |

### Fingerprint

### Keywords

- erratic nature of primes
- prime number generator
- prime number theorem
- twin primes

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016*(Vol. 1863). [560013] American Institute of Physics Inc.. https://doi.org/10.1063/1.4992696

**On the statistical distribution of prime numbers : A view from where the distribution of prime numbers are not erratic.** / Kristyán, S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016.*vol. 1863, 560013, American Institute of Physics Inc., International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016, Rhodes, Greece, 9/19/16. https://doi.org/10.1063/1.4992696

}

TY - GEN

T1 - On the statistical distribution of prime numbers

T2 - A view from where the distribution of prime numbers are not erratic

AU - Kristyán, S.

PY - 2017/7/21

Y1 - 2017/7/21

N2 - The properties of the function 2ab+a+b in the domain of natural numbers are introduced, analyzed, and exhibited to illustrate how these single out all the prime numbers from the full set of odd numbers in contrast that, it is generally said that primes show quite "erratic" distribution. The characterization of odd primes vs. odd non-primes can be done with it among the odd natural numbers as an analogue to the other, well known type of fundamental characterization for irrational and rational numbers among the real numbers. The prime number theorem, twin primes and erratic nature of primes, are also commented upon with respect to selection.

AB - The properties of the function 2ab+a+b in the domain of natural numbers are introduced, analyzed, and exhibited to illustrate how these single out all the prime numbers from the full set of odd numbers in contrast that, it is generally said that primes show quite "erratic" distribution. The characterization of odd primes vs. odd non-primes can be done with it among the odd natural numbers as an analogue to the other, well known type of fundamental characterization for irrational and rational numbers among the real numbers. The prime number theorem, twin primes and erratic nature of primes, are also commented upon with respect to selection.

KW - erratic nature of primes

KW - prime number generator

KW - prime number theorem

KW - twin primes

UR - http://www.scopus.com/inward/record.url?scp=85026626695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026626695&partnerID=8YFLogxK

U2 - 10.1063/1.4992696

DO - 10.1063/1.4992696

M3 - Conference contribution

AN - SCOPUS:85026626695

VL - 1863

BT - International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016

PB - American Institute of Physics Inc.

ER -