Dr. Preda Mihailescu                                                                                                                                                                                                                                    

Address:

Fachbereich 17 Mathematik/Informatik

Universität-GH Paderborn

D-33095 Paderborn, Germany

You can see some  pictures
You can still see my old homepage.

Research interests:

• Primality Proving (GIMPS)
• Computational Number Theory
• Cryptology
• Biometry
• Complex and numerical analysis

My Thesis:

Publications:

• P.Mihailescu. "A Primality test using cyclotomic extensions", in Applied Algebra, Algebraic Algorithms and Error - Correcting Codes, (Proceedings AAECC-6, Rome, July 1988) Lecture Notes in Comp. Sci. 357, Springer Verlag Berlin and New York, 1989, pp. 310 - 323
• P.Mihailescu. "Fast Generation of Provable Primes using Search in Arithmetic Progressions", Proceedings CRYPTO 94, Lecture Notes in Computer Science vol 939, Springer 1994, pp. 282-293. A brief description submitted for the IEEE P1363 Cryptographic standard may be downloaded here (ps, ps.gz)
• P.Mihailescu. "Cyclotomy Primality Proving - Recent Developments", Proceedings of the III Applied Number Theory Seminar, ANTS III, Portland, Oregon 1998. Lecture Notes in Computer Science vol xxx, pp y-z. ( ps , ps.gz )
• P.Mihailescu. "Recent Developments in Primality Proving" to appear in `High Performance Symbolic Computing' ( ps ,ps.gz )
• P.Mihailescu, C.Nash. "Some Facts for Lucas - Lehmer Primality Testers", preprint, 1999. ( ps , ps.gz )
• P.Mihailescu, F.Morain. "Dual Elliptic Primes and Cyclotomy Primality Proving", presented at the 6-th Conference of the Canadian Society for Number Theory, Winnipeg, 1999 . ( ps ,ps.gz ) 

  ---

Some (yet) unpublished material on Catalan's conjecture:

• P.Mihailescu: "A class number free criterion for Catalan's conjecture", to appear J. of Number Theory. ( ps , ps.gz)
• P. Mihailescu: "On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation", submitted,  J. of N.T ( ps , ps.gz ).
• P. Mihailescu: "On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation", extended version, interesting, unsubmitted ( ps , ps.gz ).
• P. Mihailescu: "Primary units and a proof of Catalan's conjecture", submitted Crelle Journal ( ps , ps.gz )

  ---

Software:

P.Mihailescu: CYCLOPROV. A LiDIA based C++ package for primality proving using cyclotomy. It was used for establishing the current record in general primality proving. It is currently available only for DEC Alpha. Download here together with the required tables. Maybe read the current `readme' first.

F.Morain: The Elliptic Curve Primality Prover ECPP.

Wei Dai: cryptlib, great freeware C++ cryptographic library. From Europe, have a look at:

V.Shoup: The NTL long integer library.

  Usefull links:

• IFWR-Homepage
• Francois Morain's ECPP (Elliptic Curve Primality Proving) home page
• Paul Leyland's Cunningham Project home page
• The Number Theory List Archives
• The GIMPS Project home page
• Chris Caldwell 's GREAT home page on Primes
• Something about Arumanians ( did you know they exist ? look at me ! )

Care to know how to laugh to the hardships of life ? You might have to learn romanian before, or try with italian first ... or have a look at the more serious french brother.

• Women REALLY Helping street children in Bucharest -  Sf. Stelian (I am a member, please ask for more  information ) .
• Fighting against BRAIN DRAINING: The  Bucharest - Ecole Normale Superieure