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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 (2^p+1)/3," J. Math. (Wuhan), 19 (1999) 199--202.  MR 2000i:11016 [The author proves the primality of (2^p+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, 2000.  Berlin, 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

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., 1990.  Providence, RI, 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

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