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

Bach85

E. Bach, Analytic methods in the analysis and design of number-theoretic algorithms, A.C.M. Distinguished Dissertations The MIT Press, 1985.  Cambridge, MA, pp. xiii+48, ISBN 0-262-02219-2. MR 87i:11185

Bach90

E. Bach, "Explicit bounds for primality testing and related problems," Math. Comp., 55:191 (1990) 355--380.  MR 91m:11096

Bach97

E. Bach, "The complexity of number-theoretic constants," Inform. Process. Lett., 62:3 (1997) 145--152.  MR 98g:11148

Bailey90

D. Bailey, "FFTs in external or hierarchical memory," Journal of Supercomputing, 4:1 (1990) 23--35.

Baillie1979

R. Baillie, "New primes of the form k · 2ⁿ + 1," Math. Comp., 33:148 (October 1979) 1333--1336.  MR 80h:10009 (Abstract available)

Balog1990

Balog, Antal, The prime k-tuplets conjecture on average.  In "Analytic number theory (Allerton {P}ark, {IL}, 1989)," Progr. Math. Vol, 85, Birkh\"auser Boston, Boston, MA, 1990.  pp. 47--75, MR 1084173

BB2000

S. Battiato and W. Borho, "Breeding amicable numbers in abundance. II," Math. Comp., 70:235 (2001) 1329--1333.  MR 2002b:11011 (Abstract available) [See [BH1986].]

BBC1999

J. M. Borwein, D. M. Bradley and R. E. Crandall, "Computational strategies for the Riemann zeta function," J. Comput. Appl. Math., 121:1--2 (2000) 247--296.  Numerical analysis in the 20th century, Vol. I, Approximation.  MR 2001h:11110

BBCGP88

P. Beauchemin, G. Brassard, C. Crépeau, C. Goutier and C. Pomerance, "The generation of random numbers that are probably prime," J. Cryptology, 1 (1988) 53--64.  MR 89g:11126

BBLR1998

E. Barcucci, S. Brunetti, A. Del Lungo and F. Del Ristoro, "A combinatorial interpretation of the recurrence f_n+1=6f_n-f_n-1," Discrete Math., 190 (1998) 235--240.  MR 99f:05001

BCEM1993

J. Buhler, R. Crandall, R. Ernvall and T. Metsänkylä, "Irregular primes and cyclotomic invariants to four million," Math. Comp., 61:203 (1993) 151--153.  MR 93k:11014

BCEMS2000

J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. Shokrollahi, "Irregular primes and cyclotomic invariants to 12 million," J. Symbolic Comput., 31:1--2 (2001) 89--96.  MR 2001m:11220

BCLK2009

A. Brunner, C. Caldwell, C. Lownsdale and D. Krywaruczenko, Generalizing sierpi\'nski numbers to base b.  In "New Aspects of Analytic Number Theory (Kyoto October 2008 proceedings)," T. Komatsu editor, RIMS, Kyoto, 2009.  pp. 69--79,

BCP82

J. P. Buhler, R. E. Crandall and M. A. Penk, "Primes of the form n! ± 1 and 2 · 3 · 5 ^... p ± 1," Math. Comp., 38:158 (1982) 639--643.  Corrigendum in Math. Comp. 40 (1983), 727.  MR 83c:10006

BCR91

R. P. Brent, G. L. Cohen and H. J. J. te Riele, "Improved techniques for lower bounds for odd perfect numbers," Math. Comp., 57:196 (1991) 857--868.  MR 92c:11004

BCS1992

J. P. Buhler, R. E. Crandall and R. W. Sompolski, "Irregular primes to one million," Math. Comp., 59:200 (1992) 717--722.  MR 93a:11106

BCW1982

R. Baillie, G. Cormack and H. C. Williams, "Corrigenda: "The problem of Sierpi\'nski concerning k· 2ⁿ+1" [Math. Comp. 37 (1981), no. 155, 229--231]," Math. Comp., 39:159 (1982) 308.  MR 83a:10006b

BCW81

Baillie, R., Cormack, G. and Williams, H.C., "The problem of Sierpinski concerning k · 2ⁿ + 1," Math. Comp., 37:155 (1981) 229--231.  MR 83a:10006a [Corrigenda: [BCW1982]]

BD1974

T. Bhargava and P. Doyle, "On the existence of absolute primes," Math. Mag., 47 (1974) 233.  MR 49:10630

Beeger50

N. G. W. H. Beeger, "On composite numbers n for which a^n-1 ≡ 1 (mod n) for every a prime to n," Scripta Math., 16 (1950) 133--135.  MR 12,159e

Beeger51

N. G. W. H. Beeger, "On even numbers m dividing 2^m - 2," Amer. Math. Monthly, 58 (1951) 553--555.  MR 13,320d

Beiler1964

A. Beiler, Recreations in the theory of numbers, Dover Pub., 1964.  New York, NY,

Benford1938

F. Benford, "The law of anomalous numbers," Proc. Amer. Math. Soc., 78 (1938) 551--572. [See [Newcomb1881]. Data partially questioned in [DF1979, p. 363].]

Bernstein1998

D. Bernstein, "Multidigit multiplication for mathematicians," Advances in Applied Mathematics, (1998) to appear? Preprint available from http://cr.yp.to/papers.html. (Abstract available) (Annotation available)

Bernstein1998b

D. Berstein, "Detecting perfect powers in essentially linear time," Math. Comp., 67:223 (1998) 1253--1283.  Available from http://cr.yp.to/papers.html.  MR 98j:11121 (Abstract available)

Bernstein2000

D. Bernstein, "How to find small factors of integers," Math. Comp.,

Bernstein2001

D. Bernstein, "Circuits for integer factorization: a proposal," (2001) Available from http://cr.yp.to/factorization.html. (Abstract available)

Bernstein2003

D. J. Bernstein, "Proving primality in essentially quartic random time," (2003) Draft available from http://cr.yp.to/papers.html.

Abstract: This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n)^4+o(1).

Berrizbeitia2003

P. Berrizbeitia, "Sharpening "Primes is in P" for a large family of numbers," (2003) Available from http://arxiv.org/abs/math.NT/0211334. (Annotation available)

BG59

C. L. Baker and F. J. Gruenberger, The first six million prime numbers, Microcard Foundation, Madison, Wisconsin, 1959.

BH1986

Borho, W. and Hoffmann, H., "Breeding amicable numbers in abundance," Math. Comp., 46:173 (1986) 281--293.  MR 87c:11003

BH1993

E. Bach and L. Huelsbergen, "Statistical evidence for small generating sets," Math. Comp., 61:203 (1993) 69--82.  MR1195432

BH1996

R. C. Baker and G. Harman, The Brun-Titchmarsh theorem on average.  In "Proc. Conf. in Honor of Heini Halberstam (Allerton Park, IL, 1995)," Progr. Math. Vol, 138, Birkhäuser Boston, 1996.  Boston, MA, pp. 39--103, MR 97h:11096

BH2000

C. Bays and R. Hudson, "A new bound for the smallest x with π(x)>li(x)," Math. Comp., 69:231 (2000) 1285--1296 (electronic).  MR1752093

BH2011

Buhler, J. P. and Harvey, D., "Irregular primes to 163 million," Math. Comp., 80:276 (2011) 2435--2444.  (http://dx.doi.org/10.1090/S0025-5718-2011-02461-0) MR 2813369

BH62

P. T. Bateman and R. A. Horn, "A heuristic asymptotic formula concerning the distribution of prime numbers," Math. Comp., 16 (1962) 363-367.  MR 26:6139

BH65

P. T. Bateman and R. A. Horn, Primes represented by irreducible polynomials in one variable.  In "Proc. Symp. Pure Math.," Vol, VIII, Amer. Math. Soc., 1965.  Providence, RI, pp. 119-132, MR 31:1234

BH77

C. Bayes and R. Hudson, "The segmented sieve of Eratosthenes and primes in arithmetic progression," Nordisk Tidskr. Informationsbehandling (BIT), 17:2 (1977) 121--127.  MR 56:5405

BH90

W. Bosma and M. P. van der Hulst, Faster primality testing.  In "Advances in Cryptology--EUROCRYPT '89 Proceedings," J. J. Quisquater and J. Vandewalle editors, Springer-Verlag, 1990.  pp. 652--656,

BH96

R. C. Baker and G. Harman, "The difference between consecutive primes," Proc. Lond. Math. Soc., series 3, 72 (1996) 261--280.  MR 96k:11111 (Abstract available)

BHV2002

Bilu, Yu., Hanrot, G. and Voutier, P. M., "Existence of primitive divisors of Lucas and Lehmer numbers," J. Reine Angew. Math., 539 (2001) 75--122.  With an appendix by M. Mignotte.  MR1863855 (Annotation available)

Biermann1964

K. R. Biermann, "Thomas Clausen: Mathematiker and Astronom," J. Reine Angew. Math., 216 (1964) 159--197.  MR 29:2153

Bleichenbacher1996

D. Bleichenbacher, "Efficiency and security of cryptosystems based on number theory," Ph.D. thesis, ETH Zürich, (1996)

BLS75

J. Brillhart, D. H. Lehmer and J. L. Selfridge, "New primality criteria and factorizations of 2^m ± 1," Math. Comp., 29 (1975) 620--647.  MR 52:5546 [The article for the classical (n² -1) primality tests. Table errata in [Brillhart1982]]

BLSTW88

J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman and S. S. Wagstaff, Jr., Factorizations of bⁿ ± 1, b=2,3,5,6,7,10,12 up to high powers, Amer. Math. Soc., Providence RI, 1988.  pp. xcvi+236, ISBN 0-8218-5078-4. MR 90d:11009 (Annotation available)

BLZ94

J. Buchmann, J. Loho and J. Zayer, An implementation of the general number field sieve, Advances in Cryptology--Crypto '93 (Santa Barbara, CA, 1993) Springer-Verlag, 1994.  New York, NY, pp. 159--165, MR 95e:11132

BM80

Brent, R. P. and McMillan, E. M., "Some new algorithms for high-precision computation of Euler's constant," Math. Comp., 34:149 (1980) 305--312.  MR 82g:10002

BMS1988

J. Brillhart, P. Montgomery and R. Silverman, "Tables of Fibonacci and Lucas factorizations," Math. Comp., 50 (1988) 251--260.  MR 89h:11002

BMS88

J. Brillhart, P. L. Montgomery and R. D. Silverman, "Tables of Fibonacci and Lucas factorizations," Math. Comp., 50 (1988) 251--260, S1--S15.  MR 89h:11002 [See also [DK99].]

BNPSSZ90

J. Brown, L. C. Noll, B. K. Parady, J. F. Smith, G. W. Smith and S. E. Zarantonello, "Letter to the editor," Amer. Math. Monthly, 97 (1990) 214. [The prime 391581 · 2²¹⁶¹⁹³ - 1 is announced]

BNW87

J. Bogoshi, K. Naidoo and J. Webb, "The oldest mathematical artefact," Math. Gazette, 71:458 (1987) 294.  MR 89a:01003

Bond84

D. J. Bond, Practical primality testing.  In "Proc. Int'l. Conf. Secure Communication Systems," IEE, 1984.  pp. 50--53,

Bone1999

C. Bone, "The Mersenne telescope," Sky \& Telescope, (September 1999) 130--133. [A variant of a design by Mersenne. This one was built with a 30-inch primary mirror.]

Boorstin1983

D. Boorstin, The discoverers, Random House Inc., New York, NY, 1983.  ISBN 0-394-40229-4.

Borning72

A. Borning, "Some results for k! ± 1 and 2 · 3 · 5 ^... p ± 1," Math. Comp., 26 (1972) 567--570.  MR 46:7133

Bosma2006

Bosma, Wieb, Some computational experiments in number theory.  In "Discovering mathematics with Magma," Algorithms Comput. Math. Vol, 19, Springer, 2006.  Berlin, pp. 1--30, MR2278921

Bosma93

W. Bosma, "Explicit primality criteria for h · 2^k ± 1," Math. Comp., 61:203 (1993) 97--109, S7--S9.  MR 94c:11005

Bowen1964

Bowen, Robert, "Mathematical Notes: The sequence kaⁿ + 1 composite for all n," Amer. Math. Monthly, 71:2 (1964) 175--176.  MR1532528

BP2001

R. Bhattacharjee and P. Pandey, "Primality testing," IIT Kanpur, (2001)

BPR96

R. Brent, A. van der Poorten and H. J. J. te Riele, A comparative study of algorithms for computing continued fractions of algebraic numbers.  In "Algorithmic Number Theory, Second International Symposium," Springer-Verlag, 1996.  Berlin, pp. 37--49, ANTS-II in Talence France, May 18-23, 1996.  MR 98c:11144

BR98

A. Björn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441--446.  MR 98e:11008 (Abstract available)

Brent1982

Brent, Richard P., "Succinct proofs of primality for the factors of some Fermat numbers," Math. Comp., 38:157 (1982) 253--255.  (http://dx.doi.org/10.2307/2007482) MR 637304

Brent73

R. P. Brent, "The first occurrence of large gaps between successive primes," Math. Comp., 27 (1973) 959-963.  MR 0330021

Brent74

R. P. Brent, "The distribution of small gaps between succesive primes," Math. Comp., 28 (1974) 315--324.  MR 48:8356

Brent75

R. P. Brent, "Irregularities in the distribution of primes and twin primes," Math. Comp., 29 (1975) 43--56.  MR 51:5522

Bressoud89

D. M. Bressoud, Factorizations and primality testing, Springer-Verlag, 1989.  New York, NY, ISBN 0387970401. MR 91e:11150 [QA161.F3B73]

Brillhart1982

Brillhart, J., "Table errata: "New primality criteria and factorizations of 2^m± 1" [Math. Comp. 29 (1975), 620--647. MR 52 \#5546. by the author, D. H. Lehmer and J. L. Selfridge," Math. Comp., 39:160 (1982) 747.  MR 83j:10010

Brillhart1999

J. Brillhart, "Note on Fibonacci primality testing," Fibonacci Quart., 36:3 (1998) 222--228.  MR1627388

Brooke1960

M. Brooke, "On the digital roots of perfect numbers," Math. Mag., 34:2 (1960) 100.  MR 23:A840

Bruce93

J. W. Bruce, "A really trivial proof of the lucas-lehmer test," Amer. Math. Monthly, 100 (1993) 370-371.  MR 94c:11006 [See also [Rosen88].]

Bruckman94a

P. S. Bruckman, "On the infinitude of Lucas pseudoprimes," Fibonacci Quart., 32 (1994) 153--154.  MR 95d:11011

Bruckman94b

P. S. Bruckman, "Lucas pseudoprimes are odd," Fibonacci Quart., 32 (1994) 155--157.  MR 95d:11012

Brun19

V. Brun, "La serie 1/5 + 1/7 + [etc.] où les denominateurs sont "nombres premiers jumeaux" est convergente ou finie," Bull. Sci. Math., 43 (1919) 100--104,124--128.

BS96

E. Bach and J. Shallit, Algorithmic number theory, Foundations of Computing Vol, I: Efficient Algorithms, The MIT Press, Cambridge, MA, 1996.  pp. xvi+512, MR 97e:11157 (Annotation available)

BSW89

P. T. Bateman, J. L. Selfridge and Wagstaff, Jr., S. S., "The new Mersenne conjecture," Amer. Math. Monthly, 96 (1989) 125-128.  MR 90c:11009

Burthe1996

R. Burthe, Jr., "Further investigations with the strong probable prime test," Math. Comp., 65:213 (1996) 373--381.  MR 96d:11137 (Abstract available)

Burton80

D. M. Burton, Elementary number theory, Allyn and Bacon, 1980.  MR 81c:10001a [Burton's texts are excellent introductions to elementary number theory and its history.]

Burton91

D. Burton, The history of mathematics, Wm. C. Brown, 1991.  MR 94b:01002

Burton97

D. M. Burton, Elementary number theory, Third edition, McGraw-Hill, 1997. [Burton's texts are excellent introductions to elementary number theory and its history.]

BW2000

D. Bressoud and S. Wagon, A course in computational number theory, Key College Publishing, 2000.  MR 2001f:11200 (Annotation available)

BW80

R. Baillie and Wagstaff, Jr., S. S., "Lucas pseudoprimes," Math. Comp., 35 (1980) 1391-1417.  MR 81j:10005

BY88

D. A. Buell and J. Young, "Some large primes and the Sierpinski problem," SRC techn. Rep. 88004, Super-Computing Res. Center, Lanham, MD, (1988)