Geodesic
The Primality of N=2A3n-1
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 585-589

Voir la notice de l'article provenant de la source Cambridge University Press

Lehmer [3] and Reisel [7] have devised tests for determining the primality of integers of the form A2n—1. Tables of primes of these forms may be found in [7] and Williams and Zarnke [10]. Little work, however, seems to have been done on integers of the form N=2A3n—1. Lucas [6] gave conditions that were only sufficient for the primality of N. Recently Lehmer [4] has given a method for determining the primality of an integer N if the factorization of N+1 is known. 
Williams, H. C. The Primality of N=2A3n-1. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 585-589. doi: 10.4153/CMB-1972-101-7
@article{10_4153_CMB_1972_101_7,
     author = {Williams, H. C.},
     title = {The {Primality} of {N=2A3n-1}},
     journal = {Canadian mathematical bulletin},
     pages = {585--589},
     year = {1972},
     volume = {15},
     number = {4},
     doi = {10.4153/CMB-1972-101-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-101-7/}
}
TY  - JOUR
AU  - Williams, H. C.
TI  - The Primality of N=2A3n-1
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 585
EP  - 589
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-101-7/
DO  - 10.4153/CMB-1972-101-7
ID  - 10_4153_CMB_1972_101_7
ER  - 
%0 Journal Article
%A Williams, H. C.
%T The Primality of N=2A3n-1
%J Canadian mathematical bulletin
%D 1972
%P 585-589
%V 15
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-101-7/
%R 10.4153/CMB-1972-101-7
%F 10_4153_CMB_1972_101_7

[1] 1. Cailler, C., Sur les congruences du troisième degré, L'Enseig. Math., 10 (1908), 474-487. Google Scholar

[2] 2. Cunningham, A. J. C., Quadratic Partitions, London, 1907. Google Scholar

[3] 3. Lehmer, D. H., An extended theory of Lucas'functions, Ann. of Math. (2), 31 (1930), 419-448. Google Scholar

[4] 4. Lehmer, D. H., Computer technology applied to the theory of numbers, M.A.A. studies in Mathematics, 6 (1969), 117-151. Google Scholar

[5] 5. Emma, Lehmer, Criteria for cubic and quartic residuacity, Mathematika 5 (1958), 20-29. Google Scholar

[6] 6. Edouard, Lucas, Théorie des functions numériques simplement périodiques, Amer. J. Math. 1 (1878), 184-240, 289-321. Google Scholar

[7] 7. Reisel, H., Lucasian criteria for the primality of N= h ⋅-2n—1, Math. Comp. 23 (1969). 869-875. Google Scholar

[8] 8. Robinson, R. M., The converse of Fermais theorem, Amer. Math. Monthly, 64 (1957), 703-710. Google Scholar

[9] 9. Smith, H. J. S., Report on the Theory of Numbers, Chelsea, New York, (1965), 103-105. Google Scholar

[10] 10. Williams, H. C. and Zarnke, C. R., A reporton primenumbersof'theforms M=(6a + 1)22m-1—1 and M' = (6a - 1)22m-1—1, Math. Comp. 22 (1968), 420-422. Google Scholar

Cité par Sources :