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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the smallest $k$ such that all $k\cdot 2^{n}+1$ are composite
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by G. Jaeschke PDF
Math. Comp. 40 (1983), 381-384 Request permission

Corrigendum: Math. Comp. 45 (1985), 637.


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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 381-384
  • MSC: Primary 10A25; Secondary 10-04
  • DOI:
  • MathSciNet review: 679453