TY - JOUR

T1 - On the density of odd integers of the form (p - 1)2-n and related questions

AU - Erdös, P.

AU - Odlyzko, A. M.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1979/5

Y1 - 1979/5

N2 - It is shown that odd integers k such that k · 2n + 1 is prime for some positive integer n have a positive lower density. More generally, for any primes p1, ..., pr, the integers k such that k is relatively prime to each of p1,..., pr, and such that k · p1n1p2n2 ... prnr + 1 is prime for some n1,..., nr, also have a positive lower density.

AB - It is shown that odd integers k such that k · 2n + 1 is prime for some positive integer n have a positive lower density. More generally, for any primes p1, ..., pr, the integers k such that k is relatively prime to each of p1,..., pr, and such that k · p1n1p2n2 ... prnr + 1 is prime for some n1,..., nr, also have a positive lower density.

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U2 - 10.1016/0022-314X(79)90043-X

DO - 10.1016/0022-314X(79)90043-X

M3 - Article

AN - SCOPUS:0013154044

VL - 11

SP - 257

EP - 263

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -