On the number of prime factors of the composite numbers resulting after a change of digits of primes
Kübra Benli1
1 Department of Mathematics University of Georgia Athens GA 30602, USA
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 K≥2, 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 2≤a≤K,0<|k|≤K,1≤j≤K,0≤h≤Klogx sont des nombres composés ayant au moins (loglogx) 1-ϵ facteurs premiers distincts.

In this note, we prove that for any fixed integer K≥2, 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,2≤a≤K,0<|k|≤K,1≤j≤K,0≤h≤Klogx are composite having at least (loglogx) 1-ϵ distinct prime factors.

Reçu le :
Révisé le :
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DOI : 10.5802/jtnb.1103
Classification : 11A41, 11P32
Mots clés : primes, digit, composite numbers
Kübra Benli 1

1 Department of Mathematics University of Georgia Athens GA 30602, USA
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     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},
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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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