Lucasian criteria for the primality of
Author:
Hans Riesel
Journal:
Math. Comp. 23 (1969), 869875
MSC:
Primary 10.08
MathSciNet review:
0262163
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Abstract: Let with given. If is a necessary and sufficient criterion that be prime, this is called a Lucasian criterion for the primality of . Many such criteria are known, but the case has not been treated in full generality earlier. A theorem is proved that (by aid of computer) enables the effective determination of suitable numbers for any given , if . The method is used on all in the domain . The Lucasian criteria thus constructed are applied, and all primes in the domain are tabulated.
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D. H. Lehmer, ``An extended theory of Lucas' functions,'' Ann. of Math., v. 31, 1930, pp. 419448.
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Edouard
Lucas, Theorie des Fonctions Numeriques Simplement Periodiques.
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1505164, http://dx.doi.org/10.2307/2369311
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Hans
Riesel, A note on the prime numbers of the forms
𝑁=(6𝑎+1)2²ⁿ⁻¹1 and
𝑀=(6𝑎1)2²ⁿ1, Ark. Mat.
3 (1956), 245–253. MR 0076793
(17,945d)
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H.
C. Williams and C.
R. Zarnke, A report on prime numbers of the forms
𝑀=(6𝑎+1)2^{2𝑚1}1 and
𝑀′=(6𝑎1)2^{2𝑚}1, Math. Comp. 22 (1968), 420–422. MR 0227095
(37 #2680), http://dx.doi.org/10.1090/S00255718196802270952
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Raphael
M. Robinson, A report on primes of the form
𝑘⋅2ⁿ+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc. 9 (1958), 673–681. MR 0096614
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 E. L. Ince, Cycles of Reduced Ideals in Quadratic Fields, British Association for the Advancement of Science, London, 1934.
 [2]
 D. H. Lehmer, ``An extended theory of Lucas' functions,'' Ann. of Math., v. 31, 1930, pp. 419448.
 [3]
 E. Lucas, ``Théorie des fonctions numériques simplement périodiques,'' Amer. J. Math., v. 1, 1878, pp. 184239, pp. 289321. MR 1505164
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 H. Riesel, ``A note on the prime numbers of the forms and ,'' Ark. Mat., v. 3, 1956, pp. 245253. MR 17, 945. MR 0076793 (17:945d)
 [5]
 H. C. Williams & C. R. Zarnke, ``A report on prime numbers of the forms and ,'' Math. Comp., v. 22, 1968, pp. 420422. MR 37 #2680. MR 0227095 (37:2680)
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 R. M. Robinson, ``A report on primes of the form and on factors of Fermat numbers,'' Proc. Amer. Math. Soc., v. 9, 1958, pp. 673681. MR 20 #3097. MR 0096614 (20:3097)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196902621631
PII:
S 00255718(1969)02621631
Article copyright:
© Copyright 1969 American Mathematical Society
