On the smallest such that all are composite
Author:
G. Jaeschke
Journal:
Math. Comp. 40 (1983), 381384
MSC:
Primary 10A25; Secondary 1004
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 is composite for all 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 is prime but is not prime for .
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Robert
Baillie, G.
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(83a:10006a), http://dx.doi.org/10.1090/S00255718198106163762
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MR
1532000, http://dx.doi.org/10.2307/2312814
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W.
Sierpiński, Sur un problème concernant les nombres
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73–74 (French). MR 0117201
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R. G. Stanton & H. C. Williams, Further Results on Coverings of the Integers by Primes, Lecture Notes in Math., vol. 884, Combinatorial Mathematics VIII, pp. 107114, SpringerVerlag, Berlin and New York, 1980.
 [1]
 R. Baillie, G. Cormack & H. C. Williams, "The problem of Sierpinski concerning ," Math. Comp., v. 37, 1981, pp. 229231. Corrigenda, Math. Comp., v. 39, 1982, p. 308. MR 616376 (83a:10006a)
 [2]
 N. S. Mendelsohn, "The equation ," Math. Mag., v. 49, 1976, pp. 3739. MR 0396385 (53:252)
 [3]
 J. L. Selfridge, "Solution to problem 4995," Amer. Math. Monthly, v. 70, 1963, p. 101. MR 1532000
 [4]
 W. Sierpinski, "Sur un probleme concernant les nombres ," Elem. Math., v. 15, 1960, pp. 7374. MR 0117201 (22:7983)
 [5]
 R. G. Stanton & H. C. Williams, Further Results on Coverings of the Integers by Primes, Lecture Notes in Math., vol. 884, Combinatorial Mathematics VIII, pp. 107114, SpringerVerlag, Berlin and New York, 1980.
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DOI:
http://dx.doi.org/10.1090/S00255718198306794538
PII:
S 00255718(1983)06794538
Article copyright:
© Copyright 1983
American Mathematical Society
