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): 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) available from http://math.univ-lille1.fr/~ramare/Maths/contenu.html..
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., Providence, RI, 1994.  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, 1994.  Boston, MA, pp. xvi+364, ISBN 0-12-587170-8. MR 95a:11029
Ribenboim1999
P. Ribenboim, Fermat's last theorem for amateurs, Springer-Verlag, New York, NY, 1999.  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, New York, 2004.  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, 1991.  New York, NY, 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 {( pn+1-pn) /log pn}.  In "Coll. Th. Nombres Bruxelles 1955," G. Thone, 1956.  Liège, 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 ap-1 ≡ 1 (mod p2) )," Math. Comp., 18 (1964) 149-150.  MR 28:1156
Riesel69
H. Riesel, "Some factors of the numbers Gn = 62n + 1 and Hn = 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 An =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, Boston, MA, 1985.  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, Boston, MA, 1994.  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, Boston, MA, 1993.  pp. xii+556, ISBN 0-12-598455-3. MR 1 247 962
Rotkiewicz1987
A. Rotkiewicz, "Note on the diophantine equation 1 + x + x2 + ... + xn = ym," 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].]
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
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