List of papers of Zhenxiang ZHANG published in international journals

(in chronological order, most recent first)

(Please email me to obtain ps or pdf files of my papers) 

• Two  kinds of strong pseudoprimes up to 10³⁶,  Mathematics of Computation, 76:260 (2007), 2095-2107.  MR2336285               http://www.ams.org/mcom/2007-76-260/S0025-5718-07-01977-1/home.html     dvi file (77kb)    

• (with Weiping Zhou and Xianbei Liu) A generalised Lucasian primality test, Bulletin of the Australian Mathematical Society, 74:3 (2006), 419-441. MR2273751 (2007i:11163)  dvi file (116kb)      

• Notes on some new kinds of pseudoprimes, Mathematics of Computation, 75:253 (2006), 451-460. MR2176408 (2006e:11013)        http://www.ams.org/mcom/2006-75-253/S0025-5718-05-01775-8/home.html    dvi file (55kb)

• Finding C₃ -strong pseudoprimes, Mathematics of Computation, 74:250 (2005), 1009-1024. MR2114662 (2005k:11243)                    http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01693-X/home.html    dvi file (104 kb)

• (with Min Tang) Finding strong pseudoprimes to several bases. II, Mathematics of Computation, 72:244 (2003), 2085-2097. MR1986825 ( 2004c :11008) http://www.ams.org/journal-getitem?pii=S0025-5718-03-01545-X     dvi file (86kb)

•   A one-parameter quadratic-base version of the Baillie-PSW probable prime test, Mathematics of Computation,71:240 (2002), 1699-1734. MR1933051 ( 2003f :11191) http://www.ams.org/journal-getitem?pii=S0025-5718-02-01424-2    dvi file (186 kb)

• Using Lucas sequences to factor large integers near group orders,  The Fibonacci Quarterly, 39:3 (2001), 228-237. MR1840030 (2002c:11173) http://www.engineering.sdstate.edu/~fib/fibprevious.html#39.3    dvi file (41 kb)  ps file of this paper available at http://www.crypto-world.com/FactorPapers.html

• Finding strong pseudoprimes to several bases, Mathematics of Computation, 70:234 (2001), 863-872. MR1697654 ( 2001g :11009)     http://www.ams.org/journal-getitem?pii=S0025-5718-00-01215-1  dvi  file (53 kb)

• Finding finite B₂-sequences with larger m-a_m^1/2, Mathematics of Computation, 63:207 (1994), 403-414. MR1223235 (94k:11109) dvi file (55kb)

• (with P.Erdös) Upper bound of  Σ 1/(a_i log a_i)  for quasi-primitive sequences, Computers Math. Applic., 26:3 (1993), 1-5. MR1221192 ( 94f :11013)

• On a problem of Erdös concerning primitive sequences, Mathematics of Computation,  60:202 (1993), 827-834. MR1181335 (93k:11120) dvi file (32 kb)

• A B₂-sequence with larger reciprocal sum, Mathematics of Computation, 60:202 (1993), 835-839. MR1181334 ( 93m :11012) dvi file (19 kb)

• (with P. Erdös)  Upper bound of  Σ 1/(a_i log a_i) for primitive sequences, Proc. Amer. Math. Soc., 117:4 (1993), 891-895. MR1116257 (93e:11018)

• On a conjecture of Erdös on the sum Σ _p<n 1/(p log p), J. Number Theory, 39:1 (1991), 14-17. MR1123165 ( 92f :11131)

！Some of my papers are cited (or referenced) in the followong books by Crandall & Pomerance, Guy and Ribenboim:

• Richard Crandall and Carl Pomerance, Primes, a computational perspective, 2nd ed., Springer-Verlag, New York, 2005.  MR2156291 (2006a:11005)

• Richard K.Guy, Unsolved problems in number theory, 3rd ed., Springer-Verlag, New York, 2004. MR2076335 (2005h:11003) (2n ed., 1994. MR 1299330 (96e:11002))

• Paulo Ribenboim, The little book of bigger primes, 2nd ed., Springer-Verlag, New York, 2004. MR2028675 (2004i:11003)

！Some of my papers are cited (or referenced) on the followong websites by Caldwell, Contini and Weisstein:

• Chris K. Caldwell, http://primes.utm.edu/glossary/page.php?sort=Pseudoprime

• Scott Contini, http://www.crypto-world.com/FactorPapers.html

• Eric W. Weisstein, http://mathworld.wolfram.com/StrongPseudoprime.html

Last updated January 17, 2008

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