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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, Martin TN, 1994.  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 A_nB, AB_n, 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 a^P-1 ≡ 1 mod P," Amer. Math. Monthly, 19 (1912) 22--27.

Carmichael19

R. D. Carmichael, "Fermat numbers F_n = 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, Bologna, 1603. (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 1_n-k-10₁1_k," J. Recreational Math., 27 (1995) 35--41.

CD97

C. Caldwell and H. Dubner, "The near repdigit primes A_n-k-1B₁A_k, especially 9_n-k-18₁9_k," 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) [Complete text: PDF]

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.

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 k^r-2ⁿ and k^r2n+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

Cohen70

H. Cohen, "On amicable and sociable numbers," Math. Comp.,:24 (1970) 423-429.

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, New York, NY, 1993.  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, New York, 2005.  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 biography.  C. Gillispie editor, Vol, IX, Amer. Council of Learned Societies, Charles Scribner's Sons, 1974.  New York, NY, 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, London, 1994.

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=(2^q ± q) and q*2^q ± 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, 1925.  London,

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 · 2^m + 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)