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The handle http://hdl.handle.net/1887/20310 holds various files of this Leiden University dissertation.

Author: Jansen, Bas

Title: Mersenne primes and class field theory

Date: 2012-12-18

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Appendix

The set of currently known exponents p ∈ Z

>0

such that 2

p

− 1 is a Mersenne prime, is

{2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609}.

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Bibliography

[1] D.A. Cox, Primes of the Form x

2

+ ny

2

, Wiley-Interscience, 1989.

[2] A. Fr¨ ohlich and M.J. Taylor, Algebraic number theory, Cambridge University Press, 1994.

[3] S.Y. Gebre-Egziabher, unpublished thesis work, U.C. Berkeley.

[4] R.K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, 1994.

[5] G. Janusz, Algebraic Number Fields, Academic Press, 1973.

[6] S. Lang, Algebra, third edition, Addison-Wesley Publishing Company, 1999.

[7] S. Lang, Algebraic Number Theory, Springer-Verlag, 1994.

[8] F. Lemmermeyer, Reciprocity laws, Springer-Verlag, 2000.

[9] H.W. Lenstra, Jr., P. Stevenhagen, Artin reciprocity and Mersenne primes, Nieuw Archief voor Wiskunde 5/1. nr.1, maart 2000, pp. 44-54.

[10] J.S. Milne, Algebraic Number Theory, http://www.jmilne.org/math, 2011.

[11] J.S. Milne, Class Field Theory, http://www.jmilne.org/math, 2011.

[12] J.S. Milne, Fields and Galois Theory, http://www.jmilne.org/math, 2011.

[13] J.R. Munkres, Topology: a first course, Prentice-Hall, 1975.

[14] J.-P. Serre, Local Fields, Springer-Verlag, 1979.

[15] J.H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer- Verlag, 1992.

[16] J.H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.

[17] A. Vardhana, personal communication, 2004.

[18] H.C. Williams, ´ Edouard Lucas and Primality Testing, Wiley-Interscience, 1998.

[19] J.S. Wilson, Profinite Groups, Oxford, 1998.

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