Number Theory


Primes Obtained Concatenating P∙q∙r-P with P∙q∙r-Q with P∙q∙r-R Then with P∙q∙r Where p, q, R Primes of the Form 6k+1

Authors: Marius Coman

This paper is inspired by one of my previous papers, namely “Large primes obtained concatenating the numbers P - d(k) where d(k) are the prime factors of the Poulet number P”, where I conjectured that there are an infinity of primes which can be obtained concatenating the numbers P - d(1); P - d(2); ...; P – d(k); P, where d(1), ..., d(k) are the prime factors of the Poulet number P. Because some of these Poulet numbers are 3-Poulet numbers of the form (6k + 1)*(6h + 1)*(6j + 1) I extend in this paper that idea conjecturing that for any prime p of the form 6k + 1 there exist an infinity of pairs of primes [q, r], of the form 6h + 1 and 6j + 1, such that the number obtained concatenating p*q*r – p with p*q*r – q with p*q*r – r then with p*q*r is prime.

Comments: 2 Pages.

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Submission history

[v1] 2017-06-06 11:10:53

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