The problem of Sierpiński concerning

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: Let be the least odd value of *k* such that is composite for all . In this note, we present the results of some extensive computations which restrict the value of to one of 119 numbers between 3061 and 78557 inclusive. Some new large primes are also given.

**[1]**G. V. Cormack and H. C. Williams,*Some very large primes of the form 𝑘⋅2^{𝑚}+1*, Math. Comp.**35**(1980), no. 152, 1419–1421. MR**583519**, https://doi.org/10.1090/S0025-5718-1980-0583519-8**[2]**P. Erdős and A. M. Odlyzko,*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**, https://doi.org/10.1016/0022-314X(79)90043-X**[3]**Richard K. Guy,*Unsolved combinatorial problems*, Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), Academic Press, London, 1971, pp. 121–127. MR**0277393****[4]**Oystein Ore, J. L. Selfridge, and P. T. Bateman,*Advanced Problems and Solutions: Solutions: 4995*, Amer. Math. Monthly**70**(1963), no. 1, 101–102. MR**1532000**, https://doi.org/10.2307/2312814**[5]**W. Sierpiński,*Sur un problème concernant les nombres 𝑘⋅2ⁿ+1*, Elem. Math.**15**(1960), 73–74 (French). MR**0117201****[6]**W. Sierpiński, 250*Problems in Elementary Number Theory*, American Elsevier, New York, 1970, p. 10 and p. 64.

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

Article copyright:
© Copyright 1981
American Mathematical Society