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): s

Saidak2005
F. Saidak, "A new proof of Euclid's theorem," Amer. Math. Monthly, 113:10 (2006) 937--938.  (http://dx.doi.org/10.2307/27642094) MR 2271540
Salas2011
Salas, Christian, "Base-3 repunit primes and the Cantor set," Gen. Math., 19:2 (2011) 103--107.  MR 2818401
Santos95
B. Santos, "Problem 2204: equidigital representations," J. Recreational Math., 21:1 (1995) 58-59. [Are there arbitrarily long sequence of economical numbers? See also [Pinch98].]
Saouter98
Y. Saouter, "Checking the odd Goldbach conjecture up to 1020," Math. Comp., 67 (1998) 863-866.  MR 98g:11115 (Abstract available)
Sayers86
M. D. Sayers, "An improved lower bound for the total number of factors of an odd perfect number," Master's thesis, M.App.Sc., NSW Inst. Tech., (1986)
Schechter1998
B. Schechter, My brain is open: the mathematical journeys of Paul Erdös, Simon \& Schuster, New York, NY, 1998.  ISBN 0-684-84635-7; 0-684-85980-7. MR 99h:01038
Schinzel1962
Schinzel, A., "On primitive prime factors of Lehmer numbers. I," Acta. Arith., 8 (1962/1963) 213--223.  MR 27:1408
Schinzel1962a
A. Schinzel, "The intrinsic divisors of Lehmer numbers in the case of negative discriminant," Ark. Mat., 4 (1962) 413--416 (1962).  MR 25:2999
Schinzel1962b
Schinzel, A., "The intrinsic divisors of Lehmer numbers in the case of negative discriminant," Ark. Mat., 4 (1962) 413--416 (1962).  MR0139567
Schinzel1963
Schinzel, A., "On primitive prime factors of Lehmer numbers. II," Acta. Arith., 8 (1962/1963) 251--257.  MR 27:1409
Schinzel1965
Schinzel, A., "On the composite Lehmer numbers with prime indices. I," Prace Mat., 9 (1965) 95--103.  MR 30:4721
Schinzel1968
Schinzel, A., "On primitive prime factors of Lehmer numbers. III," Acta Arith., 15 (1968) 49--70.  MR0232744
Schinzel1970
Schinzel, A., "Corrigendum to the papers "On two theorems of Gelfond and some of their applications" and "On primitive prime factors of Lehmer numbers. III"," Acta Arith., 16 (1969/1970) 101.  MR0246840
Schinzel1974
A. Schinzel, "Primitive divisors of the expression An - Bn in algebraic number fields," J. Reine Angew. Math., 268/269 (1974) 27--33.  MR 49:8961
Schinzel61
A. Schinzel, "Remarks on the paper `sur certaines hypothèses concernant les nombres premiers'," Acta. Arith., 7 (1961) 1--8.  MR 24:A70 [Refers to [SS58]]
Schinzel62
A. Schinzel, "On primitive prime factors of an - bn," Proc. Cambridge Phil. Soc., 58 (1962) 555--562.  MR 26:1280
Schinzel63
A. Schinzel, "A remark on a paper of Bateman and Horn," Math. Comp., 17 (1963) 445-447.  MR 27:3609
Schneier96
B. Schneier, Applied cryptography, 2nd edition, John Wiley \& Sons, 1996.  New York, NY, [A comprehensive pragmatic survey of modern cryptology--perhaps the best introduction for those actually wishing to understand the details of the usual implementations.]
Schoenfeld76
L. Schoenfeld, "Sharper bounds for the Chebyshev functions θ(x) and ψ(x) II," Math. Comp., 30:134 (April 1976) 337--360.  MR 56:15581b [Part I is [RS75].]
Schroeder83
M. R. Schroeder, "Where is the next Mersenne prime hiding?," Math. Intelligencer, 5:3 (1983) 31--33.  MR 85c:11010
Schroeder97
M. Schroeder, Number theory in science and communication : with applications in cryptography, physics, digital information, computing, and self-similarity, 3rd edition, Springer-Verlag, 1997.  New York, NY, pp. xxii+362, ISBN 3-540-62006-0. MR 99c:11165
Seelhoff1886
P. Seelhoff, "Die Zahlen von der Form k· 2n+1," Zeitschrift fur Mathematik und Physik, 31 (1886) 380.
Selberg49
A. Selberg, "An elementary proof of the prime number theorem," Ann. Math., 50 (1949) 305--313.  MR 10,595b [[HW79, sections 22.15-16] gives a slightly simpler, but less elementary version of Selberg's proof.]
Selfridge53
J. L. Selfridge, "Factors of Fermat numbers," Math. Tables Aids Comput., 7 (1953) 274-275.
Serre1974
J. P. Serre, A course in arithmetic, Springer-Verlag, 1973.  New York, NY, pp. viii+115, ISBN 0387900403. Translated from the French, Graduate Texts in Mathematics, No. 7.  MR 49:8956
SH64
J. L. Selfridge and A. Hurwitz, "Fermat numbers and Mersenne numbers," Math. Comp., 18 (1964) 146--148.  MR 28:2991
Shallit96
J. Shallit, "Minimal primes," J. Recreational Math., 30:2 (1999--2000) 113--117. [Available on-line from http://www.cs.uwaterloo.ca/~shallit/papers.html]
Shanks62
D. Shanks, "On the conjecture of hardy \& littlewood concerning the number of primes of the form n2+a," Math. Comp., 14 (1962) 321--332.  MR 22:10960
Shanks78
D. Shanks, Solved and unsolved problems in number theory, Chelsea, New York, NY, 1978.  pp. xiii+258, ISBN 0-8284-0297-3. MR 80e:10003 [QA241.S44, ISBN 0-8284-0297-3]
Shevelev2008
V. Shevelev, "Overpseudoprimes, Mersenne numbers and Wieferich primes," (July 2008) avaliable from http://arxiv.org/abs/0806.3412. (Abstract available)
Shippee1978
D. E. Shippee, "Four new factors of Fermat numbers," Math. Comp., 32:143 (1978) 941. (Abstract available)
Shurkin84
J. Shurkin, Engines of the mind: a history of the computer, W. W. Norton \& Co., 1984.
Siegel1964
C. L. Siegel, "Zu zwei Bemerkungken Kummers," Nachr. Akad. d. Wiss. Goettingen, Math. Phys. KI., II (1964) 51--62.
Sierp1069
Sierpinski, W., "Sur un probl\`eme concernant les nombres k· 2n+1," Elem. Math., 15 (1960) 73--74.  MR0117201
Sierpinski60
W. Sierpinski, "Sur un probléme concernment les nombres k · 2n +1," Elem. Math., 15 (1960) 63-74. [See the glossary entry Sierpinski number as well as the paper [Riesel56].]
Sierpinski64
W. Sierpinski, Elementary theory of numbers, Translated from Polish by A. Hulanicki. Monografie Matematyczne, Tom 42 Vol, 42, Pa\'nstwowe Wydawnictwo Naukowe, 1964.  Warsaw, pp. 480, MR 31:116
Silverman87
R. D. Silverman, "The multiple polynomial quadratic sieve," Math. Comp., 48:177 (1987) 329-339.  MR 88c:11079 [MPQS factoring method.]
Silverman88
J. H. Silverman, "Wieferich's criterion and the abc-conjecture," J. Number Theory, 30:2 (1988) 226--237.  MR 89m:11027
Simmons91
G. Simmons editor, Contemporary cryptology -- the science of information integrity, IEEE Press, 1992.  pp. xvi+640, MR 93k:94009
Sinisalo93
M. Sinisalo, "Checking the Goldbach conjecture up to 4· 1011," Math. Comp., 61:204 (1993) 931--934.  MR 94a:11157
SK1967
D. Shanks and S. Kravitz, "On the distribution of Mersenne divisors," Math. Comp., 21 (1967) 97--101.  MR0220665
SK67
D. Shanks and S. Kravitz, "On the distribution of Mersenne divisors," Math. Comp., 21 (1967) 97-101.  MR 36:3717
Sloan
N. J. A. Sloan, "The on-line encyclopedia of integer sequences," http://www.research.att.com/~njas/sequences/ (1994)
Slowinski79
D. Slowinski, "Searching for the 27th Mersenne prime," J. Recreational Math., 11 (1978-9) 258--261.
Sondow1961
J. Sondow, "Problem E1478," Amer. Math. Monthly, 68:7 (1961) 667.  Solution (with a little history): 1962, p. 235.
Spira61
R. Spira, "The complex sum of divisors," Amer. Math. Monthly, 68 (1961) 120--124.  MR 26:6101
SS1981
Shorey, T. N. and Stewart, C. L., "On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers. II," J. London Math. Soc. (2), 23:1 (1981) 17--23.  MR 82m:10025
SS58
A. Schinzel and W. Sierpinski, "Sur certaines hypotheses concernment les nombres premiers," Acta. Arith., 4 (1958) 185-208.  Erratum 5 (1958).
SS92
Z. Sun and Z. Sun, "Fibonacci numbers and Fermat's last theorem," Acta. Arith., 60 (1992) 371-388.  MR 93e:11025
Stackel1916
P. Stäckel, "Die Darstellung der geraden Zahlen als Summen von zwei Primzahlen," Sitz. Heidelberger Akad. Wiss, series Mat.-Natur. Kl., 7A:10 (1916) 1--47.
Steiner79
R. P. Steiner, "On Cullen numbers," BIT, 19:2 (1979) 276-277.  MR 80j:10009
Stevenhagen87
P. Stevenhagen, "On Aurifeuillian factorizations," Nederl. Akad. Wetensch. Indag. Math., 49:4 (1987) 451--468.  MR 89a:11015
Stewart1976
Stewart, C. L., Primitive divisors of Lucas and Lehmer numbers.  In "Transcendence theory: advances and applications (Proc. Conf., Univ. Cambridge, Cambridge, 1976)," Academic Press, London, 1977.  pp. 79--92, MR0476628
Stewart1977
C. L. Stewart, "On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers," Proc. Lond. Math. Soc., 35:3 (1977) 425--447.  MR 58:10694
Stewart1977b
Stewart, C. L., Primitive divisors of Lucas and Lehmer numbers.  In "Transcendence theory: advances and applications (Proc. Conf., Univ. Cambridge, Cambridge, 1976)," Academic Press, London, 1977.  pp. 79--92, MR 57:16187
Stewart1983
Stewart, C. L., "On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers. III," J. London Math. Soc. (2), 28:2 (1983) 211--217.  MR 85g:11021
Sun2000
Z. Sun, "On integers not of the form ± pa ± qb," Proc. Amer. Math. Soc., 128:4 (2000) 997--1002.  MR1695111 (Abstract available)
Suzuki2000
M. Suzuki, "Alternative formulations of the twin prime problem," Amer. Math. Monthly, 107:1 (2000) 55--56.  MR 2000m:11007
SW2000
A. Stein and H. C. Williams, "Explicit primality criteria for (p-1) pn-1," Math. Comp., 69 (2000) 1721--1734.  MR 2001j:11124 (Abstract available)
Szekeres96
J. Szekeres, Higher order pseudoprimes in primality testing.  In "Combinatorics, Paul Erd{\"o}s is eighty," Bolyai Soc. Math. Stud. Vol, 2, János Bolyai Math Soc., Budapest, 1996.  pp. 451--458, MR 97c:11113
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