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

Rabin80

M. O. Rabin, "Probabilistic algorithm for testing primality," J. Number Theory, 12 (1980) 128--138.  MR 81f:10003

Rademacher1977

H. Rademacher, Lectures on elementary number theory, Krieger Publishing Company, Huntington, N.Y., 1977.  pp. ix+146, ISBN 0-88275-499-8. MR 58:10677

Raimi1969

R. A. Raimi, "On the distribution of first significant figures," Amer. Math. Monthly, 76 (1969) 342--348.  MR 39:4903

Raimi1976

R. A. Raimi, "The first digit problem," Amer. Math. Monthly, 83:7 (1976) 521--538.  MR 53:14593

Ramanujan1919

S. Ramanujan, "Congruence properties of partitions," Proc. London Math. Soc., 19 (1919) 207--210.

Ramanujan1921

S. Ramanujan, "Congruence properties of partitions," Math. Z., 9 (1921) 147--153.

Ramare2002

O. Ramaré, "Éatu des lieux," (2002)

Ramare95

O. Ramaré, "On Schnirelmann's constant," Ann. Sc. Norm. Super. Pisa, 22:4 (1995) 645-706.  MR 97a:11167

RB94

H. Riesel and A. Börn, Generalized Fermat numbers.  In "Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics," W. Gautschi editor, Proc. Symp. Appl. Math. Vol, 48, Amer. Math. Soc., 1994.  Providence, RI, pp. 583-587, MR 95j:11006

Reuschle1856

K. G. Reuschle, Mathematische Abhandlung, enhaltend: Neue Zahlentheorische Tabellen, 1856.  Stuttgart,

Ribenboim1979

P. Ribenboim, 13 lectures on Fermat's last theorem, Springer-Verlag, 1979.  New York, NY, pp. xvi+302 pp. (1 plate), ISBN 0-387-90432-8. MR 81f:10023

Ribenboim1994

P. Ribenboim, Catalan's conjecture: are 8 and 9 the only consecutive powers?, Academic Press, Boston, MA, 1994.  pp. xvi+364, ISBN 0-12-587170-8. MR 95a:11029

Ribenboim1999

P. Ribenboim, Fermat's last theorem for amateurs, Springer-Verlag, 1999.  New York, NY, pp. xiv+407, ISBN 0-387-98508-5. MR 2001h:11036

Ribenboim2001

P. Ribenboim, Números primos: mistérios e recordes, Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, 2001. [A version of the text [Ribenboim95].]

Ribenboim2004

Ribenboim, P., The little book of bigger primes, Second edition, Springer-Verlag, 2004.  New York, pp. xxiv+356, ISBN 0-387-20169-6. MR2028675 [The second edititon is about 50% bigger than the first.]

Ribenboim83

P. Ribenboim, "1093," Math. Intelligencer, 5:2 (1983) 28--34.  MR 85e:11001

Ribenboim88

P. Ribenboim, The book of prime number records, 2nd edition, Springer-Verlag, New York, NY, 1988.  pp. xxiv+479, ISBN 0-387-97042-8. MR1016815 [Replaced by the text [Ribenboim95].]

Ribenboim91

P. Ribenboim, The little book of big primes, Springer-Verlag, New York, NY, 1991.  ISBN 0-387-97508-X. MR 92i:11008 (Annotation available)

Ribenboim95

P. Ribenboim, The new book of prime number records, 3rd edition, Springer-Verlag, 1995.  New York, NY, pp. xxiv+541, ISBN 0-387-94457-5. MR 96k:11112 [An excellent resource for those with some college mathematics. Basically a Guinness Book of World Records for primes with much of the relevant mathematics. The extensive bibliography is seventy-five pages.]

Ribenboim95b

P. Ribenboim, "Selling primes," Math. Mag., 68:3 (1995) 175-182.  MR 96e:11164 [Elementary introduction to finding primes; presents an algorithm to find 100 digit primes.]

Ricci56

G. Ricci, Recherches sur l'allure de la suite {( p_n+1-p_n) /log p_n}.  In "Coll. Th. Nombres Bruxelles 1955," G. Thone, Liège, 1956.  pp. 93-106,

Richards1974

Richards, Ian, "On the incompatibility of two conjectures concerning primes; a discussion of the use of computers in attacking a theoretical problem," Bull. Amer. Math. Soc., 80 (1974) 419--438.  MR 0337832

Richards74

I. Richards, "On the incompatability of two conjectures concerning primes; a discussion of the use of computers in attacking a theoretical problem," Bull. Amer. Math. Soc., 80 (1973/74) 419--438.

Richert1951

H. E. Richert, "On permutable primtall," Norsk Matematiske Tiddskrift, 33 (1951) 50--54.

Richstein2000

J. Richstein, "Verifying the goldbach conjecture up to 4· 10¹⁴," Math. Comp., 70:236 (2001) 1745--1749.  MR 2002c:11131 (Abstract available)

Riesel56

H. Riesel, "Naagra stora primtal," Elementa, 39 (1956) 258-260.  Swedish: Some large primes. [See the glossary entries Riesel number and Sierpinski number.]

Riesel58

H. Riesel, "A new Mersenne prime," Math. Tables Aids Comput., 12 (1958) 60.

Riesel58a

H. Riesel, "Mersenne numbers," Math. Tables Aids Comput., 12 (1958) 207-213.

Riesel63

H. Riesel, "A factor of the Fermat number F₁₉," Math. Comp., 17 (1963) 458.

Riesel64

H. Riesel, "Note on the congruence a^p-1 ≡ 1 (mod p²) )," Math. Comp., 18 (1964) 149-150.  MR 28:1156

Riesel69

H. Riesel, "Some factors of the numbers G_n = 6²ⁿ + 1 and H_n = 10²ⁿ + 1," Math. Comp., 23:106 (1969) 413--415.  MR 39:6813

Riesel69a

H. Riesel, "Lucasian criteria for the primality of N = h · 2ⁿ - 1," Math. Comp., 23:108 (1969) 869--875.  MR 41:6773

Riesel69b

H. Riesel, "Common prime factors of the numbers A_n =a²ⁿ+1," BIT, 9 (1969) 264-269.  MR 41:3381

Riesel85

H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics Vol, 57, Birkhäuser Boston, 1985.  Boston, MA, ISBN 0-8176-3291-3. Current edition is [Riesel94].  MR 88k:11002

Riesel94

H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics Vol, 126, Birkhäuser Boston, 1994.  Boston, MA, ISBN 0-8176-3743-5. MR 95h:11142 [An excellent reference for those who want to start to program some of these algorithms. Code is provided in Pascal. Previous edition was vol. 57, 1985.]

Robin83

G. Robin, "Estimation de la fonction de tschebyshef theta sur le k-ième nombre premier et grandes valeurs de la fonction w(n), nombre de diviseurs premiers de n," Acta. Arith., 42:4 (1983) 367-389.  MR 85j:11109

Robinson54

R. M. Robinson, "Mersenne and Fermat numbers," Proc. Amer. Math. Soc., 5 (1954) 842-846. [Announces the discovery of the 13th through 17th Mersenne primes--the first Mersenne primes found by electronic computer.]

Robinson57

R. M. Robinson, "Factors of Fermat numbers," Math. Tables Aids Comput., 11 (1957) 21-22.

Robinson57b

R. M. Robinson, "The converse of Fermat's theorem," Amer. Math. Monthly, 64 (1957) 703--710.  MR 20:4520

Robinson58

R. M. Robinson, "A report on primes of the form k· 2ⁿ + 1 and on factors of Fermat numbers," Proc. Amer. Math. Soc., 9 (1958) 673--681.  MR 20:3097

Rodine2000

C. Rodine, Marin Mersenne (1588--1648) : french mathematician and theologian.  In "Reader's Guide to the History of Science," A. Hessenbruch editor, Fitzroy Dearborn Publishers, 2000.  Illinois 60611, pp. 467--468,

Rose94

H. E. Rose, A course in number theory, second edition, Clarendon Press, 1994.  New York, pp. xvi+398, ISBN 0-19-853479-5; 0-19-852376-9. MR 96g:11001 (Annotation available)

Rosen88

M. I. Rosen, "A proof of the Lucas-Lehmer test," Amer. Math. Monthly, 95:9 (1988) 855-856.  MR 89i:11011

Ross93

S. Ross, Introduction to probability models, 5th edition, Academic Press, 1993.  Boston, MA, pp. xii+556, ISBN 0-12-598455-3. MR 1 247 962

Rotkiewicz1987

A. Rotkiewicz, "Note on the diophantine equation 1 + x + x² + ... + xⁿ = y^m," Elem. Math., 42:3 (1987) 76.  MR 88c:11020

RS62

J. B. Rosser and L. Schoenfeld, "Approximate formulas for some functions of prime numbers," Illinois J. Math., 6 (1962) 64-94.  MR 25:1139

RS75

J. B. Rosser and L. Schoenfeld, "Sharper bounds for the Chebyshev functions θ(x) and ψ(x)," Math. Comp., 29:129 (January 1975) 243--269.  MR 56:15581a [See also [Schoenfeld76].]

RT2015

Rocha, Rodrigo and Thatte, Bhalchandra, Distributed cycle detection in large-scale sparse graphs.  October 2015. (Abstract available)

Rumely83

R. Rumely, "Recent advances in primality testing," Notices Amer. Math. Soc., 30:5 (1983) 475-477.  MR 85b:11122

Russell1908

B. Russell, "Mathematical logic as based on the theory of types," Amer. J. Math., 30 (1908) 222--262.  Reprinted in B. Russell, "Logic and Knowledge," London: Allen \& Unwin, 1956, 59-102, and in J. van Heijenoort, "From Frege to Gödel," Cambridge, Mass.: Harvard University Press, 1967, 152-182..

RW1980

Rotkiewicz, A. and Wasén, R., "Lehmer's numbers," Acta Arith., 36:3 (1980) 203--217.  MR581371