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, Tome 31 (2019) no. 3, pp. 689-696.

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.

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.

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DOI : https://doi.org/10.5802/jtnb.1103
Classification : 11A41,  11P32
Mots clés : primes, digit, composite numbers
@article{JTNB_2019__31_3_689_0,
     author = {K\"ubra Benli},
     title = {On the number of prime factors of the composite numbers resulting after a change of digits of primes},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {689--696},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {3},
     year = {2019},
     doi = {10.5802/jtnb.1103},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1103/}
}
Kübra Benli. 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, Tome 31 (2019) no. 3, pp. 689-696. doi : 10.5802/jtnb.1103. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1103/

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