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Could, or should, the ancient Greeks have discovered the Lucas-Lehmer test? (English) Zbl 1384.11106

MSC:

11Y11 Primality
11A41 Primes
11-03 History of number theory
01A20 History of Greek and Roman mathematics

Citations:

Zbl 0030.01502
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Full Text: DOI

References:

[1] 1.MersenneM., Cogitata Physico Mathematica, Parisiis, 1644. Praefatio Generalis No. 19.
[2] 2.UhlerH. S., On all of Mersenne’s numbers particularly M_193, Nat. Acad. Sci., Proc., 34, (March 1948) pp. 102-103.10.1073/pnas.34.3.102 · Zbl 0030.01502
[3] 3.LucasE., Nouveaux théorèrnes d’arithrnétique supérieure, C. R. A cad. Sci. Paris, 83 (1876) pp. 1286-1288. · JFM 08.0081.02
[4] 4.LehmerD. H., On Lucas’s test for the primality of Mersenne’s numbers, J. London Math. Soc., 10 (1935) pp. 162-165. · Zbl 0012.10301
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[11] 11.RosenM. I., A proof of the Lucas-Lehmer test, The American Mathematical Monthly, 95 (1988) pp. 855-856.10.2307/2322904 · Zbl 0669.10015
[12] 12.BruceJ. W., A really trivial proof of the Lucas-Lehmer test, The American Mathematical Monthly, 100 (1993) pp. 370-371.10.2307/2324959 · Zbl 0785.11056
[13] 13.KnuthD. E., The art of computer programming, v. 2. Seminumerical Algorithms (2nd edn.), Addison-Wesley (1981). · Zbl 0477.65002
[14] 14.StehleD. and ZimmermannP., A binary recursive gcd algorithm, Algorithmic Number Theory (ANTS-VI), LNCS 3076, Springer (2004) pp.411-425. · Zbl 1125.11362
[15] 15.HardyG. H. and WrightE. M., An introduction to the theory of numbers (6th edn.) Oxford University Press (2008). · Zbl 1159.11001
[16] 16.HersteinI. N., Abstract algebra (3rd edn.), John Wiley & Sons (1996). · Zbl 0841.00004
[17] 17.CrandallR. E. and PomeranceC., Prime numbers: a computational perspective (2nd edn.), Springer, New York (2005). · Zbl 1088.11001
[18] 18.GrossB. H., An elliptic curve test for Mersenne primes, J. Number Theory, 110 (2005) pp. 114-119.10.1016/j.jnt.2003.11.011 · Zbl 1074.11065
[19] 19.LemmerrneyerF., Conics – a poor man’s elliptic curves, (2003). Available from: http://arxiv.org/pdf/math/0311306v1.pdf
[20] 20.LemmerrneyerF., Kreise und Quadrate modulo p, Mathem. Semesterberichte47 (2000) pp. 51-73.10.1007/s005910070011 · Zbl 1004.11002
[21] 21.WagstaffS. S.Jr, Divisors of Mersenne numbers, Math. Comp., 40 (1983) pp. 385-397.10.1090/S0025-5718-1983-0679454-X · Zbl 0507.10005
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