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): k

Kahan93
S. Kahan, "2--4--6--8 ldots prime gaps that appreciate," J. Recreational Math., 25 (1993) 44-46.
Kanigel1992
R. Kanigel, The man who knew infinity, Pocket Books, 1992.  New York, NY, ISBN 0671750615. MR 92e:01063
Karst1961
E. Karst, "New factors of Mersenne numbers," Math. Comp., 15 (1961) 51.  MR0116481
Karst1962
E. Karst, "Search limits on divisors of Mersenne Numbers," Nordisk Tidskr. Informations-Behandling, 2 (1962) 224--227.  MR0166144
Karst73
E. Karst, Prime factors of Cullen numbers n· 2n± 1.  In "Number Theory Tables," A. Brousseau editor, Fibonacci Assoc., 1973.  San Jose, CA, pp. 153--163,
Keller83
W. Keller, "Factors of Fermat numbers and large primes of the form k· 2n +1," Math. Comp., 41 (1983) 661-673.  MR 85b:11117
Keller88
W. Keller, "The least prime of the form k· 2n + 1 for certain values of k," Abstracts Amer. Math. Soc., 9 (1988) 417--418.
Keller91
W. Keller, "Woher kommen die größten derzeit bekannten Primzahlen?," Mitt. Math. Ges. Hamburg, 12:2 (1991) 211-229.  MR 92j:11006
Keller92
W. Keller, "Factors of Fermat numbers and large primes of the form k· 2n + 1 ii," Hamburg, (September 1992) Manuscript.
Keller95
W. Keller, "New Cullen primes," Math. Comp., 64 (1995) 1733-1741.  Supplement S39-S46.  MR 95m:11015
Keller98
W. Keller, "Prime solutions p of ap-1≡ (mod p2) for prime bases a," Abstracts Amer. Math. Soc., 19 (1998) 394.
KLS2001
M. Krízek, F. Luca and L. Somer, 17 lectures on Fermat numbers: from number theory to geometry, CMS Books in Mathematics Vol, 9, Springer-Verlag, 2001.  New York, NY, pp. xvii + 257, ISBN 0-387-95332-9. MR 2002i:11001
Knuth75
D. E. Knuth, The art of computer programming. Volume 1: fundamental algorithms, Addison-Wesley, Reading, Mass., 1975.  pp. xxii+634, 2nd edition, 2nd printing.  MR 51:14624
Knuth81
D. E. Knuth, Seminumerical algorithms, 2nd edition, The Art of Computer Programming Vol, 2, Addison-Wesley, Reading MA, 1981.  MR 83i:68003 [This book is an excellent reference for anyone interested in the basic aspects of programming the algorithms mentioned in these pages. New edition: [Knuth97]]
Knuth97
D. E. Knuth, Seminumerical algorithms, 3rd edition, The Art of Computer Programming Vol, 2, Addison-Wesley, 1997.  Reading MA, [This book is an excellent reference for anyone interested in the basic aspects of programming the algorithms mentioned in these pages.]
Koblitz87
N. Koblitz, A course in number theory and cryptology, Springer-Verlag, 1987.  New York, NY,
Kolata94
G. Kolata, "The assault on 114,381,625,757,888,867,669,235,779,976,146,612,010,218, 296,721,242,362,562,561,842,935,706,935,245,733,897,830,597,123,563,958,705,058, 989,075,147,599,290,026,879,543,541," New York Times, March 22 1994, p.~B5.
Kolata94a
G. Kolata, "100 quadrillion calculations and, Eureka! problem solved," New York Times, April 27 1994, p.~A11.
Kolberg1959
O. Kolberg, "Note on the parity of the partition function," Math. Scand., 7 (1959) 377--378.  MR0117213
Konyagin1999
S. V. Konyagin, "Estimates of the least prime factor of a binomial coefficient," Mathematika, 46:1 (1999) 41--55.  MR1750402
KP89
S. H. Kim and C. Pomerance, "The probability that a random probable prime is composite," Math. Comp., 53 (1989) 721-741.  MR 90e:11190
KP96
S. Konyagin and C. Pomerance, On primes recognizable in deterministic polynomial time.  In "The Mathematics of Paul Erd{\"o}s," Algorithms Combin. Vol, 13, Springer-Verlag, Berlin, 1996.  pp. 176--198, MR 98a:11184
KR98
W. Keller and J. Richstein, "Prime solutions p of ap-1≡ 1 (mod p2) for prime bases a, II," Abstracts Amer. Math. Soc., (1998) submitted.
KR98a
R. Kumanduri and C. Romero, Number theory with computer applications, Prentice Hall, Upper Saddle River, New Jersey, 1998.
Kra2005
B. Kra, "The Green-Tao theorem on arithmetic progressions in the primes: an ergodic point of view," Bull. Amer. Math. Soc., 43:1 (2006) 3--23 (electronic).  (http://dx.doi.org/10.1090/S0273-0979-05-01086-4) MR 2188173 (Abstract available)
Kraitchik1924
M. Kraitchik, Recherches sur la th'eorie des nombres, W. W. Norton \& Co., Vol, 1, Gauthier-Vilars, 1924.
Kraitchik52
M. Kraitchik, Introduction à la théorie des nombres, Gauthier-Villars, 1952.  Paris, pp. 2, 8.
Kravitz1961
S. Kravitz, "Divisors of Mersenne numbers 10,000<p<15,000," Math. Comp., 15 (1961) 292--293.  MR0123508
Krizek2008
M. Křížek and L. Somer, "Euclidean primes have the minimum number of primitive roots," JP J. Algebra Number Theory Appl., 12:1 (2008) 121--127.  MR2494078
KS2002
N. Kayal and N. Saxena, "Towards adeterministic polynomial-time test," (2002) Available from http://www.cse.iitk.ac.in/research/btp2002/primality.html.
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