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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the smallest $ k$ such that all $ k\cdot 2\sp{n}+1$ are composite


Author: G. Jaeschke
Journal: Math. Comp. 40 (1983), 381-384
MSC: Primary 10A25; Secondary 10-04
Corrigendum: Math. Comp. 45 (1985), 637.
MathSciNet review: 679453
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Abstract: In this note we present some computational results which restrict the least odd value of k such that $ k \cdot {2^n} + 1$ is composite for all $ n \geqslant 1$ to one of 91 numbers between 3061 and 78557,inclusive. Further, we give the computational results of a relaxed problem and prove for any positive integer r the existence of infinitely many odd integers k such that $ k\cdot{2^r} + 1$ is prime but $ k\cdot{2^v} + 1$ is not prime for $ v < r$.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0679453-8
PII: S 0025-5718(1983)0679453-8
Article copyright: © Copyright 1983 American Mathematical Society