The problem of Sierpiński concerning $k\cdot 2^{n}+1$

Authors:
Robert Baillie, G. Cormack and H. C. Williams

Journal:
Math. Comp. **37** (1981), 229-231

MSC:
Primary 10A25

DOI:
https://doi.org/10.1090/S0025-5718-1981-0616376-2

Corrigendum:
Math. Comp. **39** (1982), 308.

Corrigendum:
Math. Comp. **39** (1982), 308.

MathSciNet review:
616376

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Abstract | References | Similar Articles | Additional Information

Abstract: Let ${k_0}$ be the least odd value of *k* such that $k \cdot {2^n} + 1$ is composite for all $n \geqslant 1$. In this note, we present the results of some extensive computations which restrict the value of ${k_0}$ to one of 119 numbers between 3061 and 78557 inclusive. Some new large primes are also given.

- G. V. Cormack and H. C. Williams,
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*On the density of odd integers of the form $(p-1)2^{-n}$ and related questions*, J. Number Theory**11**(1979), no. 2, 257–263. MR**535395**, DOI https://doi.org/10.1016/0022-314X%2879%2990043-X - Richard K. Guy,
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*Problems in Elementary Number Theory*, American Elsevier, New York, 1970, p. 10 and p. 64.

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Article copyright:
© Copyright 1981
American Mathematical Society