Number Theory

    

An Unusual Conjecture on Primes Involving Concatenation and Repunits

Authors: Marius Coman

In this paper I make the following conjecture: for any k positive integer there exist an infinity of primes p such that the number q, obtained concatenating (p – k) with p then, repeatedly k times, with the digit 1, is prime. Examples: for k = 1, there exist p = 19 such that q = 18191 is prime; for k = 2, there exist p = 5 such that q = 3511 is prime; for k = 3, there exist p = 7 such that q = 47111 is prime; for k = 4, there exist p = 37 such that q = 33371111 is prime; for k = 5, there exist p = 11 such that q = 61111111 is prime; for k = 6, there exist p = 17 such that q = 1117111111 is prime.

Comments: 2 Pages.

Download: PDF

Submission history

[v1] 2016-04-01 02:05:48

Unique-IP document downloads: 143 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus