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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, 1998.  New York, NY, 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, New York, NY, 1973.  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, Warsaw, 1964.  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, 1977.  London, 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 ± p^a ± q^b," 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., 1996.  Budapest, pp. 451--458, MR 97c:11113