I have grown to enjoy the web as my primary place to
publish, but as an academic it is necessary to also necessary publish
through refereed and edited media. Below I list most of my traditional publications.
- C. Caldwell and Y. Xiong, "What is the smallest prime?," J. Int. Sequences, 15:article 12.9.7 (2012) 1--14. (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell1/cald5.html)
- C. Caldwell, Y. Xiong, A. Reddick and W. Keller, "The history of the primality of one: a selection of sources," J. Int. Sequences, 15:article 12.9.8 (2012) 1--40. (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.html)
- C. Caldwell and A. Rupinski, "Pyramids of 3-powerful-primes," Math. Spectrum, 43:2 (2010-2011) 65--69.
- C. Caldwell and T. Komatsu, "Powers of Sierpinski numbers base B," Integers, 10 (2010) A36, 423--436. (http://dx.doi.org/10.1515/INTEG.2010.036) MR 2684132
- C. Caldwell and T. Komatsu, "Some periodicities in the continued fraction expansions of Fibonacci and Lucas Dirichlet series," Fibonacci Quart., 48:1 (2010) 47--55. MR 2663419
- C. Caldwell and G. L. Honaker, Jr., Prime Curios! The Dictionary of Prime Number Trivia, CreateSpace, 2009. pp. x+306 pages, ISBN 978-1-448-65170-2. October 2009.. [This is a selection of the Prime Curios! expanded, supplemented, and printed as a book: https://www.createspace.com/3392450]
- A. Brunner, C. Caldwell, C. Lownsdale and D. Krywaruczenko, Generalizing sierpi\'nski numbers to base b. In "New Aspects of Analytic Number Theory (Kyoto October 2008 proceedings)," T. Komatsu editor, RIMS, Kyoto, 2009. pp. 69--79,
- C. Caldwell,"Marin Mersenne" in The Biographical Encyclopedia of Astronomers. Vol, 2, Springer-Verlag, 2007. pp. 772--773, ISBN 978-0-387-31022-0.
- C. Caldwell and Y. Cheng, "Determining Mills' constant and a note on Honaker's problem," J. Integer Seq., 8:4 (2005) Article 05.4.1, 9 pp. (electronic). Available from http://www.cs.uwaterloo.ca/journals/JIS/. MR2165330 (Abstract available)
- C. Caldwell, [Japanese: Encyclopedia of the Prime Numbers], Kyoritsu Shuppan, 2004. pp. xv+385 pages, ISBN 4-320-01759-5. Translated by SOJIN. [This is a Japanese translation of a subset of my web pages published in book form.]
- C. Caldwell and Y. Gallot, "On the primality of n! ± 1 and 2 × 3 × 5 × ^{...} × p ± 1," Math. Comp., 71:237 (2002) 441--448. MR 2002g:11011 (Abstract available) (Annotation available)
- C. Caldwell and G. L. Honaker, Jr., "Is π(6521)=6!+5!+2!+1! unique?," Math. Spectrum, 22:2 (2000/2001) 34--36. Preprint available online at http://www.utm.edu/~caldwell/preprints/.
- G. L. Honaker, Jr. and C. Caldwell, "Palindromic prime pyramids," J. Recreational Math., 30:3 (1999-2000) 169--176. (Annotation available)
- C. Caldwell and H. Dubner, "Primes in pi," J. Recreational Math., 29 (1998) 282--289.
- C. Caldwell and H. Dubner, "Unique period primes," J. Recreational Math., 29:1 (1998) 43--48.
- C. Caldwell, "Unique (period) primes and the factorization of cyclotomic polynomial minus one," Mathematica Japonica, 46:1 (1997) 189--195. MR 99b:11139 (Abstract available)
- C. Caldwell, "Getting close to the million-digit prime," J. Recreational Math., 28:4 (1996--97) 242.
- C. Caldwell, "New largest known prime," J. Recreational Math., 28:1 (1996--97) 17.
- C. Caldwell and H. Dubner, "The near repdigit primes A_{n-k-1}B_{1}A_{k}, especially 9_{n-k-1}8_{1}9_{k}," J. Recreational Math., 28:1 (1996-97) 1--9.
- C. Caldwell, "On the primality of n! ± 1 and 2 · 3 · 5 ^{...} p ± 1," Math. Comp., 64:2 (1995) 889--890. MR 95g:11003
- C. Caldwell, "Prime words," J. Recreational Math., 27:1 (1995) 49--57. [See the page "prime words."]
- C. Caldwell and H. Dubner, "The near repunit primes 1_{n-k-1}0_{1}1_{k}," J. Recreational Math., 27 (1995) 35--41.
- C. Caldwell, Discovering number theory, Ossuary Press, Martin TN, 1994. pp. xxxviii+125, [Entirely activity based number theory course using UBASIC]
- C. Caldwell, "The diophantine equation A! B! = C!," J. Recreational Math., 26:2 (1994) 128--132.
- C. Caldwell, "UBASIC," J. Recreational Math., 25:1 (1993) 47--54. [A 2600 digit version of BASIC available on the web with the APRT-CL primality test, MPQS and ECM factoring methods included.]
- C. Caldwell, "A new record prime," J. Recreational Math., 25:4 (1993) 262. Letter to the editor.
- C. Caldwell, "The Dubner PC Cruncher--a microprocessor card for doing integer arithmetic," J. Recreational Math., 25:1 (1993) 56--57. [Hardware/software review]
- C. Caldwell and H. Dubner, "Primorial, factorial and multifactorial primes," Math. Spectrum, 26:1 (1993/4) 1--7.
- C. Caldwell, "A generalization of a result of Hurwitz and Mordell on the torsion subgroups of certain elliptic curves," Rocky Mountain J. Math., 22:1 (1992) 93--108. MR 93e:11071
- C. Caldwell, "Teaching discovery: an example using computers in number theory," PRIMUS, II:3 (1992) 203--212.
- C. Caldwell, "A polynomial inequality quickie, problem q776," Math. Mag., 26:2 (1991) 132, 137.
- C. Caldwell, "The near repdigit primes A_{n}B, AB_{n}, and UBASIC," J. Recreational Math., 22:2 (1990) 100--109.
- C. Caldwell, "Nice polynomials of degree four," Math. Spectrum, 23:2 (1990/91) 36--39.
- C. Caldwell, "Problem: minimal rulers," J. Recreational Math., 22:1 (1990) 23.
- C. Caldwell, "Solution to problem 1717: a reciprocal diophantine equation," J. Recreational Math., 22:2 (1990) 156--157.
- C. Caldwell, "The near repdigit primes 333 ^{...} 331," J. Recreational Math., 21:4 (1989) 299--304.
- C. Caldwell, "Problem 1717: a reciprocal diophantine equation," J. Recreational Math., 21:2 (1989) 145.
- C. Caldwell, A method to teach number theory using a computer. In "The Proccedings of the Conference on Technology in Collegiate Mathematics: The Twilight of the Pencil and Paper," Addison-Wesley, New York, NY, 1989. pp. 122--125,
- C. Caldwell, "Permutable primes," J. Recreational Math., 19:2 (1987) 135--138. [Discusses permutable primes such as 733 in base 10, and 742 in base 13.]
- C. Caldwell, "Truncatable primes," J. Recreational Math., 19:1 (1987) 30--33. [A recreational note discussing left truncatable primes, right truncatable primes, and deletable primes.]
- C. Caldwell, Polynomials of one variable: the theory of equations, Ossuary Press, Martin TN, 1987.