Reference Database
(references for the Prime Pages)
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This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

All items with keys beginning with the letter(s): c

Caldwell1987
C. Caldwell, Polynomials of one variable: the theory of equations, Ossuary Press, Martin TN, 1987.
Caldwell1989
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, 1989.  New York, NY, pp. 122--125,
Caldwell1991
C. Caldwell, "Nice polynomials of degree four," Math. Spectrum, 23:2 (1990/91) 36--39.
Caldwell1992
C. Caldwell, "Teaching discovery: an example using computers in number theory," PRIMUS, II:3 (1992) 203--212.
Caldwell1992a
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
Caldwell1993
C. Caldwell, "The Dubner PC Cruncher--a microprocessor card for doing integer arithmetic," J. Recreational Math., 25:1 (1993) 56--57. [Hardware/software review]
Caldwell1994
C. Caldwell, "The diophantine equation A! B! = C!," J. Recreational Math., 26:2 (1994) 128--132.
Caldwell1994a
C. Caldwell, Discovering number theory, Ossuary Press, 1994.  Martin TN, pp. xxxviii+125, [Entirely activity based number theory course using UBASIC]
Caldwell1995
C. Caldwell, "Prime words," J. Recreational Math., 27:1 (1995) 49--57. [See the page "prime words."]
Caldwell2004
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.]
Caldwell2007
C. Caldwell,"Marin Mersenne" in The Biographical Encyclopedia of Astronomers.  Vol, 2, Springer-Verlag, 2007.  pp. 772--773, ISBN 978-0-387-31022-0.
Caldwell87
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.]
Caldwell87a
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.]
Caldwell89
C. Caldwell, "The near repdigit primes 333 ... 331," J. Recreational Math., 21:4 (1989) 299--304.
Caldwell90
C. Caldwell, "The near repdigit primes AnB, ABn, and UBASIC," J. Recreational Math., 22:2 (1990) 100--109.
Caldwell93
C. Caldwell, "UBASIC," J. Recreational Math., 25:1 (1993) 47--54. [A 2600 digit version of BASIC with the APRT-CL primality test, MPQS and ECM factoring methods included.]
Caldwell95
C. Caldwell, "On the primality of n! ± 1 and 2 · 3 · 5 ... p ± 1," Math. Comp., 64:2 (1995) 889--890.  MR 95g:11003
Caldwell97
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)
Card1968
Card, "Patterns in primes," J. Recreational Math., 1 (1968) 93--99.
Carlitz1954
L. Carlitz, "Note on irregular primes," Proc. Amer. Math. Soc., 5 (1954) 329--331.  MR 15,778b
Carmichael12
R. D. Carmichael, "On composite numbers P which satisfy the Fermat congruence aP-1 ≡ 1 mod P," Amer. Math. Monthly, 19 (1912) 22--27.
Carmichael19
R. D. Carmichael, "Fermat numbers Fn = 22n + 1," Amer. Math. Monthly, 26 (1919) 137--146.
Carmichael1913
R. D. Carmichael, "On the numerical factors of the arithmetic forms αn ± βn," Ann. Math., 15 (1913) 30--70.
Catalan1844
E. Catalan, "Note extraite d'une lettre adressée à l'édite," J. reine angew. Mathematik, 27 (1844) 192.
Cataldi1603
P. A. Cataldi, Trattato de nvmeri perfetti di Pietro Antonio Cataldo, Presso gli Heredi di Giovanni Rossi, 1603.  Bologna, (Annotation available)
CB90
G. Cassella and R. Berger, Statistical inference, Statistics--Probability Series Brooks/Cole, 1990.  MR 91j:62002
CC2005
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)
CD1998
C. Caldwell and H. Dubner, "Unique period primes," J. Recreational Math., 29:1 (1998) 43--48.
CD2000
C. Caldwell and H. Dubner, "Primes in pi," J. Recreational Math., 29 (1998) 282--289.
CD93
C. Caldwell and H. Dubner, "Primorial, factorial and multifactorial primes," Math. Spectrum, 26:1 (1993/4) 1--7.
CD95
C. Caldwell and H. Dubner, "The near repunit primes 1n-k-1011k," J. Recreational Math., 27 (1995) 35--41.
CD97
C. Caldwell and H. Dubner, "The near repdigit primes An-k-1B1Ak, especially 9n-k-1819k," J. Recreational Math., 28:1 (1996-97) 1--9.
CDNY95
R. Crandall, J. Doenias, C. Norrie and J. Young, "The twenty-second Fermat number is composite," Math. Comp., 64 (1995) 863--868.  MR 95f:11104
CDP97
R. Crandall, K. Dilcher and C. Pomerance, "A search for Wieferich and Wilson primes," Math. Comp., 66:217 (1997) 433--449.  MR 97c:11004 (Abstract available)
CF94
R. Crandall and B. Fagin, "Discrete weighted transforms and large-integer arithmetic," Math. Comp., 62:205 (1994) 305--324.  MR 94c:11123
CFJJK2006
Csajbók, T., Farkas, G., Járai, A., Járai, Z. and Kasza, J., "Report on the largest known Sophie Germain and twin primes," Ann. Univ. Sci. Budapest. Sect. Comput., 26 (2006) 181--183.  MR 2388687
CG2000
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)
CGH95
G. Cohen, S. Gretton and P. Hagis, Jr., "Multiamicable numbers," Math. Comp., 64 (1995) 1743--1753.  MR 95m:11012
CGSS1997
Conway, John H., Guy, Richard K., Schneeberger, W. A. and Sloane, N. J. A., "The primary pretenders," Acta Arith., 78:4 (1997) 307--313.  MR 1438588
CH2009
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]
Chamberland2003
Chamberland, Marc, "Binary BBP-formulae for logarithms and generalized Gaussian-Mersenne primes," Journal of Integer Sequences, 6:Article 03.3.7 (2003) 1--10.  http://www.emis.ams.org/journals/JIS/VOL6/Chamberland/chamberland60.pdf.
Chen2000
Chen, Yong-Gao, "On integers of the form 2k± pα11 pα22 ... pαrr," Proc. Amer. Math. Soc., 128:6 (2000) 1613--1616.  MR1695159
Chen2001a
Chen, Yong-Gao, "On integers of the forms k-2n and k2n+1," J. Number Theory, 89:1 (2001) 121--125.  MR1838707
Chen2001b
Chen, Yong-Gao, "On integers of the form k2n+1," Proc. Amer. Math. Soc., 129:2 (2001) 355--361 (electronic).  MR1800230
Chen2003
Chen, Yong-Gao, "On integers of the forms kr-2n and kr2n+1," J. Number Theory, 98:2 (2003) 310--319.  MR1955419
Chen2007
Chen, Yong-Gao, "On integers of the forms k± 2n and k2n± 1," J. Number Theory, 125:1 (2007) 14--25.  MR2333115
Cheng2000
Y. Cheng, "An explicit zero-free region for the Riemann zeta-function," Rocky Mountain J. Math., 30:1 (2000) 135--148.  MR 2001k:11165 (Abstract available)
Cheng2003
Q. Cheng, "Primality proving via one round of ECPP and one iteration in AKS," Crypto 2003, Santa Barbara, (2003) Available from http://www.cs.ou.edu/~qcheng/.
Cheng2003a
Cheng, Yuan-You Fu-Rui, "Explicit estimate on primes between consecutive cubes," Rocky Mountain J. Math., 40:1 (2010) 117--153.  (http://dx.doi.org/10.1216/RMJ-2010-40-1-117) MR 2607111
Chernick39
J. Chernick, "On Fermat's simple theorem," Bull. Amer. Math. Soc., 45 (1939) 269--274.
Cherwell46
Lord Cherwell, "Note on the distribution of the intervals between primes numbers," Quart. J. Math. Oxford, 17:65 (1946) 46--62.  MR 8,136e
Chowla44
S. Chowla, "There exists an infinity of 3--combinations of primes in A. P.," Proc. Lahore Phil. Soc., 6 (1944) 15--16.  MR 7,243l
Cipolla1902
M. Cipolla, "La determinatzione assintotica dell`n^imo numero primo," Matematiche Napoli, 3 (1902) 132--166.
CK1984
D. Cohen and K. Talbot, "Prime numbers and the first digit phenomenon," J. Number Theory, 18 (December 1984) 261--268.  MR 85j:11014
CK2009a
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
CK2010
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
CL84
H. Cohen and Lenstra, Jr., H. W., "Primality testing and Jacobi sums," Math. Comp., 42 (1984) 297--330.  MR 86g:11078 [APRT-CL test introduced.]
CL87
H. Cohen and A. K. Lenstra, "Implementation of a new primality test," Math. Comp., 48 (1987) 103--121.  MR 88c:11080 [APRT-CL test implemented.]
Clark1973
H. J. Clark, "Letter to the editor," Computer Weekly,:360 (27 September 1973) 26.
Clawson1996
C. C. Clawson, Mathematical mysteries, Plenum Press, New York, NY, 1996.  pp. x+313, ISBN 0-306-45404-1. MR 98e:11001
Clement1949
P. A. Clement, "Congruences for sets of primes," Amer. Math. Monthly, 56 (1949) 23--25.  MR 10,353f
CMP2003
R. E. Crandall, E. W. Mayer and J. S. Papadopoulos, "The twenty-fourth Fermat number is composite," Math. Comp., 72 (2003) 1555--1572. (Abstract available)
Cohen1976
D. Cohen, "An explanation of the first digit phenomenon," J. Combin. Theory, Ser. A, 20 (1976) 367--370.  MR 53:10698
Cohen87
G. L. Cohen, "On the largest component of an odd perfect number," J. Austral. Math. Soc. Ser. A, 42 (1987) 280--286.  MR 87m:11005
Cohen93
H. Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics Vol, 138, Springer-Verlag, 1993.  New York, NY, MR 94i:11105
Conrey89
B. Conrey, "More than two fifths of the zeros of the Riemann zeta function are on the critical line," J. Reine Angew. Math., 399 (1989) 1-26.  MR 90g:11120
Corput1939
A. G. van der Corput, "Über Summen von Primzahlen und Primzahlquadraten," Math. Ann., 116 (1939) 1--50.
CP2001
R. Crandall and C. Pomerance, Prime numbers: a computational perspective, Springer-Verlag, 2001.  New York, NY, pp. xvi+545, ISBN 0-387-94777-9. MR 2002a:11007 (Abstract available) [This is a valuable text written by true experts in two different areas: computational and theoretical respectively. There is now a second edition [CP2005].]
CP2005
R. Crandall and C. Pomerance, Prime numbers--a computational approach, Second edition, Springer, 2005.  New York, pp. xvi+597, ISBN 978-0-387-25282-7; 0-387-25282-7. MR2156291
CR2009
C. Caldwell and A. Rupinski, "Pyramids of 3-powerful-primes," Math. Spectrum, 43:2 (2010-2011) 65--69.
Cramer36
H. Cramér, "On the order of magnitude of the differences between consecutive prime numbers," Acta. Arith., 2 (1936) 396-403.
Crandall96
R. Crandall, Topics in advanced scientific computation, Springer-Verlag, 1996.  MR 97g:65005
Crombie1974
A. C. Crombie,"Marin Mersenne" in Dictionary of scientific biographyC. Gillispie editor, Vol, IX, Amer. Council of Learned Societies, Charles Scribner's Sons, New York, NY, 1974.  pp. 316--322, ISBN 0-684-10120-3.
Crombie1994
A. C. Crombie, Styles of scientific thinking in the european tradition: the history of argument and explanation especially in the mathematical and biological sciences and arts, Duckworth, 1994.  London,
CRXK2012
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)
CS1975
F. Cohen and J. L. Selfridge, "Not every number is the sum or difference of two prime powers," Math. Comp., 29 (1975) 79--81.  Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday.  MR0376583 (Abstract available)
CS2005
D. A. Cox and J. Shurman, "Geometry and number theory on clovers," Amer. Math. Monthly, 112:8 (2005) 682--704.  MR2167769
Cullen05
J. Cullen, "Question 15897," Educ. Times, (December 1905) 534. [Originated the study of Cullen numbers. See also [CW17].]
Cunningham06
A. Cunningham, "Solution of question 15897," Math. Quest. Educ. Times, 10 (1906) 44--47. (Annotation available)
Cunningham13
A. Cunningham, On Mersenne's numbers.  In "Proc. 5th International Congress of Mathematicians," E. W. Hobson and A. E. H. Love editors, Vol, I, Cambridge University Press, 1913.  pp. 384--386,
Cunningham1907
A. Cunnningham, "On hyper-even numbers and on Fermat's numbers," Proc. Lond. Math. Soc., series 2, 5 (1907) 237--274.
Cunningham1927
A. J. C. Cunningham, Quadratic and linear tables, F. Hodgson, 1927.
Cutter2001
P. Cutter, "Finding prime pairs with particular gaps," Math. Comp., 70:235 (2001) 1737--1744.  MR 2002c:11174 (Abstract available)
CW04
A. Cunningham and A. E. Western, "On Fermat's numbers," Proc. Lond. Math. Soc., 1 (1904) 175.
CW17
A. J. C. Cunningham and H. J. Woodall, "Factorisation of Q=(2q ± q) and q*2q ± 1," Math. Mag., 47 (1917) 1--38. [A classic paper in the history of the study of Cullen numbers. See also [Keller95]]
CW1996
Chen, Jing Run and Wang, Tian Ze, "The Goldbach problem for odd numbers," Acta Math. Sinica (Chin. Ser.), 39:2 (1996) 169--174.  MR1411958 (Abstract available)
CW25
A. J. C. Cunningham and H. J. Woodall, Factorizations of yn -/+ 1, y = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers (n), Hodgson, London, 1925.
CW60
Lord Cherwell and E. M. Wright, "The frequency of prime-patterns," Quart. J. Math. Oxford, series 2, 11 (1960) 60--63.  MR 24:A98
CW80
G. V. Cormack and H. C. Williams, "Some very large primes of the form k · 2m + 1," Math. Comp., 35 (1980) 1419--1421.  MR 81i:10011
CW89
J. R. Chen and Y. Wang, "On the odd Goldbach problem," Acta Math. Sinica, 32 (1989) 702--718.
CW91
W. N. Colquitt and Welsh, Jr., L., "A new Mersenne prime," Math. Comp., 56 (1991) 867--870.  MR 91h:11006 [The discovery of the 29th Mersenne prime.]
CX2012
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)
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