[For Farey fractions and Riemann hypothesis see Uniform distribution and prime numbers.] -------------------------------------------------- 1967 H. Aboud: The greatest prime divisor of an arithmetic sequence. Vestnik Mosk. Univ. Mat. 44/6 (1989), 3-7. 29068 Christian Aebi/Grant Cairns: Catalan numbers, primes and twin primes. Elem. Math. 63/4 (2008), 153-164. 1755 P. Alexandrov (ed.): Die Hilbertschen Probleme. Leipzig 1983. 26371 Levent Alpoge: Van der Waerden and the primes. Am. Math. Monthly 122/8 (2015), 784-785. A proof of the infinitude of the set of primes by van der Waerden's theorem. 17840 Eleonora Andreotti: Esistono infinite progressioni aritmetiche di numeri primi di lunghezza k per ogni intero positivo. Elaborazione di una conferenza sul teorema di Green-Tao. Aprile 2006, 14p. 26919 Christian Axler: Über die Primzahlzählfunktion, die n-te Primzahl und verallgemeinerte Ramanujan-Primzahlen. Diss. Univ. Düsseldorf 2013, 140p. 26918 Christian Axler: New bounds for the prime counting function \pi(x). Arxiv 1409.1780 (2016), 10p. 22864 Paul Bateman/Harold Diamond: A hundred years of prime numbers. Am. Math. Monthly 103/9 (1996), 729-741. 25287 P. Bateman/John Selfridge/S. Wagstaff: The new Mersenne conjecture. Amer. Math. Monthly 96/2 (1989), 125-128. 4074 Christoph Baxa: Ueber Gandhis Primzahlformel. El. Math. 47 (1992), 82-84. [7922] 26914 Carter Bays/Richard Hudson: A new bound for the smallest x with \pi(x)>li(x). Math. Comp. 69/231 (1999), 1285-1296. 3071 Maria Bedendo: La dimostrazione elementare del teorema dei numeri primi. Tesi, Ferrara 1989. 2001 Edmondo Bedocchi: Nota ad una congettura sui numeri primi. Riv. Mat. Univ. Parma 11 (1985), 229-236. A. Blanchard: Introduction a' la theorie analytique des nombres premiers. Dunod 1969. 20119 Valentin Blomer: The theorem of Green-Tao. EMS Newsletter March 2008, 13-16. 22910 Wolfgang Blum: Goldbach und die Zwillinge. Spektrum Dezember 2008, 94-99. 24883 Andrew Booker: On Mullin's second sequence of primes. Integers 12A (2012), 10p. 17751 Folkmar Bornemann/Günter Ziegler: Die Beweise des Sommers. DMV-Mitt. 12/3 (2004), 181-183. 7746 D. Borwein/J. Borwein/P. Borwein/R. Girgensohn: Giuga's conjecture on primality. Am. Math. Monthly (1996), 40-50. 25285 Kevin Broughan/Qizhi Zhou: Flat primes and thin primes. Internet 2008, 16p. 29094 Chris Caldwell/Yves Gallot: On the primality of n!+/-1 and 2x3x5x...xp+/-1. Math. Comp. 71 (2002), 441-448. 23311 Chris Caldwell/G. Honaker: Prime curios! CreateSpace 2009, 300p. Eur 18. A small encyclopedia of (about 1100) interesting prime numbers. 24872 Nathan Carlson: A connection between Furstenberg's and Euclid's proofs of the infinitude of primes. Am. Math. Monthly 121/ (2014), 444. 26471 Timothy Choi: Notes on Wolstenholme's theorem. Internet 2008, 2p. 25313 James Clarkson: On the series of prime reciprocals. Proc. AMS 17 (1966), 541. A short proof of the divergence of the series. 14472 Henri Cohen: Zahlentheoretische Aspekte der Kryptographie. Informatik-Spektrum Juni 2001, 129-139. David Conlon/Jacob Fox/Yufei Zhao: The Green-Tao theorem - an exposition. EMS Surveys Math. Sci. 1/2 (2014), 249-282. D. Cox: Primes of the form x^2+ny^2. Fermat, class field theory and complex multiplication. Wiley 1989, 350p. Pds. 35. 20297 David Cox: Visualizing the sieve of Eratosthenes. Notices AMS May 2008, 579-582. 19112 Richard Crandall/Carl Pomerance: Prime numbers. Springer 2005, 600p. Eur 62. 1929 Harold Davenport: Multiplicative number theory. Springer 1980. 7861 M. Deleglise/J. Rivat: Computing \pi(x): The Meissel, Lehmer, Lagarias, Miller, Odlyzko method. Math. Comp. 65 (1996), 235-245. 16648 John Derbyshire: Prime obsession. Plume 2004, 410p. $11. 362 H. Diamond: Elementary methods in the study of the distibution of prime numbers. Bull. AMS 7 (1982), 553-589. H. Dubner/H. Nelson: Seven consecutive primes in arithmetic progression. Math. Comp. ... (1997), ... 26952 Anthony Edwards: Infinite coprime sequences. Math. Gazette 48 (1964), 416-422. 361 William Ellison/Fern Ellison: Prime numbers. Wiley 1985. Benjamin Fine/Gerhard Rosenberger: Number theory - an introduction via the distribution of primes. Birkhäuser 2006, 320p. $50. 8760 Tony Forbes: Large prime triples. Mail to nmbrthry@listserv.nodak.edu, 6 December 1996, 2p. 5493 Peter Giblin: Primes and programming. Cambridge UP 1993. G. Giuga: Su una presumibile proprieta' caratteristica dei numeri primi. Ist. Lombardo Sci. Lett. Rend. A 83 (1950), 511-528. 26912 Larry Goldstein: A history of the prime number theorem. Am. Math. Monthly 80/6 (1973), 599-615. 27365 Solomon Golomb: Arithmetica topologica. In Gen. Top. Rel. Mod. An. Algebra 1961, 179-186. [Furstenbergs topology on the integers.] 20985 Andrew Granville: Prime number patterns. Am. Math. Monthly 115 (2008), 279-296. 26320 Andrew Granville: The anatomy of integers and permutations. Internet ca. 2009, 16p. 21971 Andrew Granville: Different approaches to the distribution of primes. Milan J. Math. 78 (2010), 65-84. 26913 Andrew Granville: What is the best approach to counting primes? Internet 2014, 33p. E. Grassini: I numeri composti m che verificano la congruenza di Fermat (a^{m-1}=1, mod m). Period. Mat. 43 (1965), 183-208. 17068 Ben Green: Linear equations in the primes: past, present and future. Internet 2005, 15p. 17069 Ben Green/Terence Tao: The primes contain arbitrarily long arithmetic progressions. Ann. Math. 167 (2008), 481-547. 1994 R. Guy/C. Lacampagne/John Selfridge: Primes at a glance. Math. Computation 48 (1987), 183-202. 16626 Julian Havil: Gamma. Exploring Euler's constant. Princeton UP 2003, 260p. $21. 1908 D. Heath-Brown: Differences between consevutive primes. Jber. DMV 90 (1988), 71-89. G. Helmberg: Analytische Zahlentheorie. De Gruyter 2018, 100p. Eur 35. 26487 Charles Helou/Guy Terjanian: On Wolstenholme's theorem and its converse. J. Number Theory 128 (2008), 475-499. 7863 Edmund Hlawka: Erinnerungen an Karl Prachar. Monatshefte 121 (1996), 1-9. 1880 Loo-Keng Hua: Additive Primzahltheorie. Leipzig 1959. A. Ingham: On two conjectures in the theory of numbers. Am. J. Math. 64 (1942), 313-319. G. Jameson: The prime number theorem. Cambridge UP, 260p. Pds. 19. 20663 James Jones/Daihachiro Sato/Hideo Wada/Douglas Wiens: Diophantine representation of the set of prime numbers. Am. Math. Monthly 83 (1976), 449-464. Knopfmacher: Abstract analytic number theory. Dover. 0-486-66344-2. $ 10. D. Koukoulopoulos: The distribution of prime numbers. AMS 2019, 360p. Gerd Kowol: Primzahlen. Phil.-Anthrop. Verlag, Dornach 1995, 170p. DM 37. 17677 Bryna Kra: The Green-Tao theorem of arithmetic progressions in the primes - an ergodic point of view. Bull. AMS 43/1 (2006), 3-23. 7812 Martin Kutrib/Joerg Richstein: Primzahlen - Zwillinge aus dem Parallelrechner. Spektrum 1996/2, 26-31. Das Sieb des Eratosthenes eignet sich recht gut zur Parallelisierung. 26803 Jeffrey Lagarias: Euler's constant - Euler's work and modern developments. arXiv: 1303.1856 (2013), 93p. Very interesting. 363 Edmund Landau: Handbuch der Lehre von der Verteilung der Primzahlen. Chelsea 1974. 26700 Alessandro Languasco/Alessandro Zaccagnini: A note on Mertens' formula for arithmetic progressions. J. Number Theory 127 (2007), 37-46. 23740 Alessandro Languasco/Alessandro Zaccagnini: Explicit relations between primes in short intervals and exponential sums over primes. Internet 2012, 12p. H. Lenstra: Factoring integers with elliptic curves. Annals Math. 126 (1987), 649-673. Norman Levinson: A motivated account of an elementary proof of the prime numbers. Am. Math. Monthly 76 (1969), 225-245. The most elementary of the elementary proofs. Gu''nter Loh: Long chains of nearly doubled primes. Math. Comp. 53 (1989), 751-759. Yu. Matijasevich: Diophantine representation of the set of prime numbers. Dokl. Akad. Nauk SSSR 196 (1971), 770-773. Russian. 2056 C. Matthews: Matrix prime number theorems. Proc. Japan Ac. 65 A (1989), 336-339. 20187 Barry Mazur: Finding meaning in error terms. Bull. AMS 45/2 (2008), 185-228. 26909 Barry Mazur/William Stein: Prime numbers and the Riemann hypothesis. Cambridge UP 2016, 140p. Eur 27. [23667 Barry Mazur/William Stein: Primes. Internet (draft) 2013, 140p.] 1977 A. Mercier: Relations between \omega(n) and \Omega(n). Am. Math. Monthly 97 (1990), 503-505. [3323] 26470 Romeo Mestrovic: Wolstenholme's theorem - its generalizations and extensions in the last hundred and fifty years (1862-2012). Internet 2012, 30p. 1945 Hugh Montgomery: Topics in multiplicative number theory. SLN Math. 227 (1986). 1937 Yoichi Motohashi: Sieve methods and prime number theory. Springer 1983. M. Nair: On Chebyshev-type inequalities for primes. Am. Math. Monthly 89 (1982), 126-129. Wladyslaw Narkiewicz: The development of prime number theory. Springer 2010, 460p. Eur 161. Probably very beautiful, but at a preposterous price. 24884 Eric Naslund: The average largest prime factor. Integers 13 (2013), 5p. 22863 D. Newman: Simple analytic proof of the prime number theorem. Am. Math. Monthly 87 (1980), 693-696. 25922 Marius Overholt: A course in analytic number theory. AMS 2014, 370p. Eur 70. 4549 Herbert Pieper: Zahlen aus Primzahlen. Birkhäuser 1984. 21827 Friedrich Pillichshammer: Die Verteilung der Primzahlen. Internet 2008, 68p. 17067 Christoph Pöppe: Arithmetische Primzahlfolgen beliebiger Länge. Spektrum 2005/4, 114-117. Ben Green und Terence Tao haben bewiesen, daß es arithmetische Folgen beliebiger Länge gibt, die nur aus Primzahlen bestehen. Die längste bekannte derartige Folge wurde von Markus Frind, Paul Jobling und Paul Underwood gefunden; sie besteht aus den 23 Primzahlen 56211383760397 + 44546738095860 k für k=0,...,22. 24875 Paul Pollack/Enrique Trevino: The primes that Euclid forgot. Am. Math. Monthly 121/ (2014), 433-437. 22570 Carl Pomerance: The prime number graph. Math. Comp. 33 (1979), 399-408. The author studies the set of all (n,p_n). 25296 Carl Pomerance: Prime numbers and the search for extraterrestrial intelligence. In D. Hayes/T. Shubin: Mathematical adventures for students and amateurs. MAA 2004, 4p. Carl Pomerance/R. Crandall: Primes. Springer 1999, 350p. 3-540-94777-9. DM 98. 411 Karl Prachar: Primzahlverteilung. Springer 1957. 7889 Karl Prachar: Bemerkungen ueber Primzahlen in kurzen Reihen. Acta Arithm. 44 (1984), 175-180. 15982 Paulo Ribenboim: 1093. Boll. UMI Mat. Soc. Cult. 6/A (2003), 165-182. 1093 is the smallest prime p with the property that 2^{p-1} is congruent to 1 mod p^2. Paulo Ribenboim: The little book of bigger primes. Springer 2004, 350p. Eur 50. 26622 Paulo Ribenboim: Die Welt der Primzahlen. 2. Auflage. Springer 2011, 380p. Eur 25 (Ebuch). 27191 Herman te Riele: On the sign of the difference \pi(x)-li(x). Math. Comp. 48/177 (1987), 323-328. Dan Rockmore: Stalking the Riemann hypothesis. Pantheon 2005, 300p. $17. A non-technical historical account. 22571 J. Rosser/Lowell Schoenfeld: Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), 64-94. O. Sacks: The man who mistook his wife for a hat. Picador, London 1986. Probably a book on autistic persons. Contains the story of autistic twins John and Michael, who were able to recognize large primes (of 6 to 10 digits) simply by looking at them. Reference found in Peter Giblin's book "Primes and programming" (Cambridge UP 1993). 24389 Marcus du Sautoy: The music of the primes. Harper 2011, 250p. Eur 11. 5740 Wolfgang Schwarz: Der Primzahlsatz. 5738 Laugwitz, 35-61. 410 Wolfgang Schwarz: Einfuehrung in Methoden und Ergebnisse der Primzahltheorie. Bibl. Inst. 1969. 409 Wolfgang Schwarz: Über einige Probleme aus der Theorie der Primzahlen. Steiner 1985. 23337 Wolfgang Schwarz: Skript Primzahltheorie. Internet 2007, 37p. M. Shai Haran: The mysteries of the real prime. Oxford UP 2001, 250p. Pds. 45. 25284 Tarlok Shorey: Some topics in prime number theory. Math. Newsletter Ramanujan Math. Soc. 18 (2008), 62-67. 26920 Stanley Skewes: On the difference \pi(x)-li(x). J. London MS 8 (1933), 277-283. 26921 Stanley Skewes: On the difference \pi(x)-li(x) II. Proc. London MS 5 (1955), 48-70. 26236 Jaime Sorenson: A review of prime patterns. Internet 2008, 7p. 24060 Joel Spencer/Ronald Graham: The elementary proof of the prime number theorem. Math. Intell. ... (2009), 6p. 4806 Harold Stark: Galois theory, algebraic number theory, and zeta functions. 4740 Waldschmidt, 313-393. 25349 Zhi-Wei Sun: Conjectures involving primes and quadratic forms. Internet 2013, 34p. 25348 Zhi-Wei Sun: Problems on combinatorial properties of primes. Internet 2014, 19p. 22972 Terence Tao: The dichotomy between structure and randomness, arithmetic progressions, and the primes. Internet 2005, 27p. 22992 Terence Tao: Multiscale analysis of the primes. Internet, ca. 2006, 27p. 25371 Terence Tao: Obstructions to uniformity and arithmetic patterns in the primes. Pure Appl. Math. Quarterly 2/2 (2006), 395-433. 22249 Terence Tao/Ernest Croot/Harald Helfgott: Deterministic methods to find primes. Math. Computation ... (2011), 14p. 25604 Terence Tao/Tamar Ziegler: The primes contain arbitrarily long polynomial progressions. Internet 2013, 82p. 26747 Terence Tao/Tamar Ziegler: Polynomial patterns in the primes. Internet 2016, 46p. G. Tenenbaum: Introduction to analytic and probabilistic number theory. Cambridge UP 1995, 450p. 0-521-41261-7. Pds. 45. 25315 Gerald Tenenbaum/Michel Mendes France: The prime numbers and their distribution. AMS 2001, 114p. Eur 20. "In diesem Büchlein wird auf knappen 127 Seiten ein erstaunlich tiefgehender Überblick über die analytische Primzahltheorie gegeben ... Es ist ein großer Genuß, in diesem Buch zu schmökern." (M. Drmota) 1895 Ernst Trost: Primzahlen. Birkhaeuser 1968. 18140 Yuri Tschinkel: About the cover - on the distribution of primes - Gauss' tables. Bull. AMS 43/1 (2006), 89-91. R. Vaughan: Mean value theorems in prime number theory. J. LMS 10 (1975), 153-162. R. Vaughan: An elementary method in prime number theory. Acta Arithm. 37 (1980), 111-115. 26235 Carlos Vinuesa: Asymptotics for magic squares of primes. Internet 2012, 34p. 25797 Albert Leon Whiteman: Review of the book "Primzahlverteilung" by Karl Prachar. Bull. AMS 64 (1958), 113-119. 26468 Wikipedia: Wolstenholme's theorem. Wikipedia 2015, 4p. 26469 Wikipedia: Satz von Wolstenholme. Wikipedia 2015, 3p. 23988 Wolfgang Willems: Primzahlen sind der Wahnsinn. Internet, 5p. 25309 M. Wolf: Computer experiments with Mersenne primes. CMST 19/3 (2013), 157-165. 2046 Dieter Wolke: Ueber die Primteiler-Anzahl \omega(n). Monatshefte Math. 110 (1990), 73-78. [3323] 1969 D. Wolke: Ueber die zahlentheoretische Funktion \omega(n). Acta Arithmetica 55 (1990), 323-331. [3323] 1970 J. Wu: Sur la suite des nombres premiers jumeaux. Acta arithmetica 55 (1990), 365-394. 1972 Ti Zuo Xuan: The average order of d(k,n) over integers free of large prime factors. Acta Arithmetica 55 (1990), 249-260. [3323] 19245 Alessandro Zaccagnini: Primes in almost all short intervals. Acta Arithmetica 84/3 (1998), 225-244. 19297 Alessandro Zaccagnini: Introduzione alla teoria analitica dei numeri. Corso Univ. Parma 2006, 53p. 29486 Alessandro Zaccagnini: Breve storia dei numeri primi. Internet 2014, 17p. 26915 Alessandro Zaccagnini: I numeri primi - teoremi, congetture e applicazioni. Internet 2016, 14p. Don Zagier: Die ersten 50 Millionen Primzahlen. 1847 Borho, 39-73. 22862 Don Zagier: Newman's short proof of the prime number theorem. Am. Math. Monthly 104/8 (1997), 705-708. Hans Zassenhaus: Ueber die Existenz von Primzahlen in arithmetischen Progressionen. Comm. Math. Helv. 22 (1949), 232-259. The first elementary proof of Dirichlet's theorem. 26492 ZZ: GIMPS project discovers largest known prime number. Science Daily 20 January 2016, 3p. The prime is 2^{74207281}-1.