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): pq

Paxson61
G. A. Paxson, "The compositeness of the thirteenth Fermat number," Math. Comp., 15 (1961) 420.
Pepin77
T. Pepin, "Sur la formule 22n+1," C. R. Acad. Sci. Paris, 85 (1877) 329-331.
Pepin78
T. Pepin, "Sur la formule 2n - 1," C. R. Acad. Sci. Paris, 86 (1878) 307-310.
Peretti1987
Peretti, A., "The quantity of Sophie Germain primes less than x," Bull. Number Theory Related Topics, 11:1-3 (1987) 81--92.  MR 995537
Peterson2000
I. Peterson, "Prime proof zeros in on crucial numbers," Science News, 158 (December 2000) 357.  Short note that Miailescu showed solutions to Catalan's are Wierferich double primes.
Peterson85
I. Peterson, "Prime time for supercomputers," Science News, 128 (1985) 199.
Peterson88
I. Peterson, "Priming for a lucky strike," Science News, 133 (1988) 85.
Peterson92
I. Peterson, "Striking paydirt in prime-number terrain," Science News, 141:14 (1992) 213. [Discusses the discovery of the Mersenne prime 2756839 -1]
Peterson93
I. Peterson, "Dubner's primes," Science News, 144:21 (1993) 331. [Discusses the Dubner Cruncher [DD85] and a few of Dubner's record primes.]
PH2002
Perschell, Karaloine and Huff, Loran, "Mersenne primes in imaginary quadratic number fields," (2002) avaliable from http://www.utm.edu/staff/caldwell/preprints/kpp/Paper2.pdf. (Abstract available)
Pi1998
Pi, Xin Ming, "Searching for generalized Fermat primes," J. Math. (Wuhan), 18:3 (1998) 276--280.  MR 1656292
Pi1999
X. M. Pi, "Primes of the form (2p+1)/3," J. Math. (Wuhan), 19 (1999) 199--202.  MR 2000i:11016 [The author proves the primality of (2p+1)/3 for p=1709 and 2617.]
Pi2002
Pi, Xin Ming, "Generalized Fermat primes for b < 2000, m< 10," J. Math. (Wuhan), 22:1 (2002) 91--93.  MR 1897106
Picutti1989
E. Picuttii, "Pour l'histoire des sept premiers nombres parfaits," Historia Mathematica, 16 (1989) 123--136.
Pierpont1895
J. Pierpont, "On an undemonstrated theorem of the Disquisitiones Aritmeticae," American Mathematical Society Bulletin,:2 (1895-1896) 77 - 83.
Pinch2000
R. Pinch, The pseudoprimes up to 1013.  In "Algorithmic number theory (Leiden, 2000)," Lecture Notes in Comput. Sci. Vol, 1838, Springer-Verlag, Berlin, 2000.  pp. 459--473, MR 2002g:11177
Pinch93
R. Pinch, "The Carmichael numbers up to 1015," Math. Comp., 61:203 (1993) 381-391.  MR 93m:11137 [A preprint and several data files may be found in the Carmichael directory of his FTP site. For example, he lists the Carmichaels to 1017.]
Pinch93a
R. G. E. Pinch, "Some primality testing algorithms," Notices Amer. Math. Soc., 40 (1993) 1203-1210. [This article describes the primality testing algorithms in use in some popular computer algebra systems, and gives examples where they break down in practice.]
Pinch98
R. Pinch, "Economical numbers," (1998) preprint. (Annotation available)
Platt2012
D. J. Platt, "Computing π(x) analytically," preprint. Available from http://arxiv.org/abs/1203.5712.
PMT95
P. Pritchard, A. Moran and A. Thyssen, "Twenty-two primes in arithmetic progression," Math. Comp., 64:211 (1995) 1337--1339.  MR 95j:11003
Abstract: Some newly-discovered arithmetic progressions of primes are presented, including five of length twenty-one and one of length twenty-two.
Pocklington14
H. C. Pocklington, "The determination of the prime or composite nature of large numbers by Fermat's theorem," Proc. Cambridge Phil. Soc., 18 (1914-1916) 29-30.
Pollard74
J. Pollard, "Theorems of factorization and primality testing," Proc. Cambridge Phil. Soc., 76 (1974) 521-528. [Pollard introduces his p-1 factoring method.]
Pollard75
J. Pollard, "Monte Carlo method for factorization," BIT, 15 (1975) 331-334. [Pollard introduces his rho method.]
Polya59
G. Pólya, "Heuristic reasoning in the theory of numbers," Amer. Math. Monthly, 66 (1959) 375-384.
Pomerance1986
C. Pomerance, "On primitive divisors of Mersenne numbers," Acta Arith., 46:4 (1986) 355--367.  MR871278
Pomerance81
C. Pomerance, "Recent developments in primality testing," Math. Intelligencer, 3:3 (1980/81) 97--105.  MR 83h:10015
Pomerance82
C. Pomerance, "The search for prime numbers," Scientific American, 247:6 (December 1982) 136-147,178.
Pomerance84
C. Pomerance, Lecture notes on primality testing and factoring (notes by G. M. Gagola Jr.), Notes Vol, 4, Mathematical Association of America, 1984.  pp. 34 pages,
Pomerance94
C. Pomerance, Lecture notes in primality testing and factoring--a short course at Kent State University, MAA Notes Vol, 4, MAA, 1984. [ISBN 0-88358-054-0]
Pomerance94a
C. Pomerance editor, Cryptology and computational number theory--an introduction, Proc. Symp. Appl. Math. Vol, 42, Amer. Math. Soc., Providence, RI, 1990.  pp. 1--12, MR 92e:94023
Poussin1989
C. de la Vallée Poussin, "Sur les valeurs moyennes de certaines fonctions arithmétiques," Annales de la société scientifique de Bruxelles, 22 (1898) 84--90.
Powers11
R. E. Powers, "The tenth perfect number," Amer. Math. Monthly, 18 (1911) 195-197.
Powers14
R. E. Powers, "On Mersenne's numbers," Proc. Lond. Math. Soc., 13 (1914) xxxix.
Pritchard87
P. Pritchard, "Linear prime-number sieves: a family tree," Sci. Comput. Programming, 9:1 (1987) 17--35.  MR 88j:11087 [A comparison of recent sieves such as the sieve of Eratosthenes.]
Proth1878
F. Proth, "Théorèmes sur les nombres premiers," C. R. Acad. Sci. Paris, 85 (1877) 329-331.
PS2002
A. Paszkiewicz and A. Schinzel, "On the least prime primitive root modulo a prime," Math. Comp., 71:239 (2002) 1307--1321.  MR 2003d:11006 (Abstract available)
PSS89
J. Pintz, W. L. Steiger and E. Szemerédi, "Infinite sets of primes with fast primality tests and quick generation of large primes," Math. Comp., 53:187 (1989) 399-406.  MR 90b:11141
PSW80
C. Pomerance, J. L. Selfridge and Wagstaff, Jr., S. S., "The pseudoprimes to 25 · 109," Math. Comp., 35:151 (1980) 1003-1026.  MR 82g:10030 [See Richard Pinch's lists of pseudoprimes and [Jaeschke93].]
PSZ90
B. K. Parady, J. F. Smith and S. E. Zarantonello, "Largest known twin primes," Math. Comp., 55 (1990) 381-382.  MR 90j:11013
PTVF93
W. Press, S. Teukolsky, W. Vetterling and B. Flannery, Numerical recipes in C : the art of scientific computing, Cambridge University Press, 1993.  pp. xxvi+963, ISBN 0-521-43108-5. MR 93i:65001b
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