Volume 12 - Issue 4 (2) | PP: 164 - 168
Language : English

DOI : https://doi.org/10.31559/glm2022.12.4.2

DOI : https://doi.org/10.31559/glm2022.12.4.2

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#### When Doesn’t the Interval [an+k + Pn, an+k+1 + Pn] (n, k 2 N) Contain any Primes? Theorem and Counterexamples (an is the nth Prime Number & Pn is the nth Prime Factorial)

Received Date | Revised Date | Accepted Date | Publication Date |

6/11/2022 | 21/12/2022 | 27/12/2022 | 31/12/2022 |

##### Abstract

###### The objective of this short paper is to give and prove a main theorem confirming that any interval of the special form: ]an+k + Pn, an+k+1 + Pn[ (n 2 N) does not contain any primes, for all k 2 N such that an+k+1 < a2 n+1 (an is the nth prime number & Pn is the nth prime factorial). Then we give several counterexamples of such intervals, which contain primes, when the condition (an+k+1 < a2 n+1) is not satisfied.

##### How To Cite This Article

Rezgui , H. (2022). When Doesn’t the Interval [an+k + Pn, an+k+1 + Pn] (n, k 2 N) Contain any Primes? Theorem and Counterexamples (an is the nth Prime Number & Pn is the nth Prime Factorial). General Letters in Mathematics, 12 (4), 164-168, 10.31559/glm2022.12.4.2

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