On the number of prime factors of the composite numbers resulting after a change of digits of primes
Journal de théorie des nombres de Bordeaux, Volume 31 (2019) no. 3, pp. 689-696.

In this note, we prove that for any fixed integer K2, for all ϵ>0 and for all sufficiently large x, there exist at least x 1-ϵ primes x<p(1+K -1 )x, such that all of the integers pj±a h k,2aK,0<|k|K,1jK,0hKlogx are composite having at least (loglogx) 1-ϵ distinct prime factors.

Dans cette note, nous prouvons que pour tout entier fixé K2, pour tout ϵ>0 et pour tout x suffisamment grand, il existe au moins x 1-ϵ nombres premiers x<p(1+K -1 )x tels que tous les nombres entiers de la forme pj±a h k avec 2aK,0<|k|K,1jK,0hKlogx sont des nombres composés ayant au moins (loglogx) 1-ϵ facteurs premiers distincts.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1103
Classification: 11A41,  11P32
Keywords: primes, digit, composite numbers
Benli, Kübra 1

1 Department of Mathematics University of Georgia Athens GA 30602, USA
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Benli, Kübra. On the number of prime factors of the composite numbers resulting after a change of digits of primes. Journal de théorie des nombres de Bordeaux, Volume 31 (2019) no. 3, pp. 689-696. doi : 10.5802/jtnb.1103. http://www.numdam.org/articles/10.5802/jtnb.1103/

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