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Mathematics of Computation

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On the smallest $k$ such that all $k\cdot 2^{n}+1$ 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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Article copyright: © Copyright 1983 American Mathematical Society