Geodesic
Sequences with Translates Containing Many Primes
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 15-19

Voir la notice de l'article provenant de la source Cambridge University Press

Garrison [3], Forman [2], and Abel and Siebert [1] showed that for all positive integers $k$ and $N$ , there exists a positive integer $\lambda $ such that ${{n}^{k}}\,+\,\lambda $ is prime for at least $N$ positive integers $n$ . In other words, there exists $\lambda $ such that ${{n}^{k}}\,+\,\lambda $ , represents at least $N$ primes.We give a quantitative version of this result.We show that there exists $\lambda \le {{x}^{k}}$ such that ${{n}^{k}}\,+\,\lambda $ , 1 ≤ n ≤ x, represents at least $\left( \frac{1}{k}\,+\,o\left( 1 \right) \right)\,\pi \left( x \right)$ primes, as $x\to \infty $ . We also give some related results.
DOI : 10.4153/CMB-1998-003-3
Mots-clés : 11A48 
Brown, Tom; Shiue, Peter Jau-Shyong; Yu, X.Y. Sequences with Translates Containing Many Primes. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 15-19. doi: 10.4153/CMB-1998-003-3
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