04339nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245008600160250001700246260004800263300003300311505022800344505095400572505098501526653001802511653002502529653001802554653002502572710003402597041001902631989003802650856007202688082001002760520125502770EB000618293EBX0100000000000000047137500000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814612075971 aRibenboim, Paulo00aThe New Book of Prime Number RecordshElektronische Ressourcecby Paulo Ribenboim a3rd ed. 1996 aNew York, NYbSpringer New Yorkc1996, 1996 aXXIV, 541 pbonline resource0 aIII. Polynomials with Many Successive Composite Values -- IV. Partitio Numerorum -- V. Some Probabilistic Estimates -- Conclusion -- The Pages That Couldn’t Wait -- Primes up to 10,000 -- Index of Tables -- Index of Names0 aIV. Prime-Producing Polynomials -- 4 How Are the Prime Numbers Distributed? -- I. The Growth of ?(x) -- II. The n th Prime and Gaps -- Interlude -- III. Twin Primes -- Addendum on k-Tuples of Primes -- IV. Primes in Arithmetic Progression -- V. Primes in Special Sequences -- VI. Goldbach’s Famous Conjecture -- VII. The Waring-Goldbach Problem -- VIII. The Distribution of Pseudoprimes, Carmichael Numbers, and Values of Euler’s Function -- 5 Which Special Kinds of Primes Have Been Considered? -- I. Regular Primes -- II. Sophie Germain Primes -- III. Wieferich Primes -- IV. Wilson Primes -- V. Repunits and Similar Numbers -- VI. Primes with Given Initial and Final Digits -- VII. Numbers k×2n±1 -- VIII. Primes and Second-Order Linear Recurrence Sequences -- IX. The NSW Primes -- 6 Heuristic and Probabilistic Results about Prime Numbers -- I. Prime Values of Linear Polynomials -- II. Prime Values of Polynomials of Arbitrary Degree -- 0 a1 How Many Prime Numbers Are There? -- I. Euclid’s Proof -- II. Goldbach Did It Too! -- III. Euler’s Proof -- IV. Thue’s Proof -- V. Three Forgotten Proofs -- VI. Washington’s Proof -- VII. Fürstenberg’s Proof -- VIII. Euclidean Sequences -- IX. Generation of Infinite Sequences of Pairwise Relatively Prime Integers -- 2 How to Recognize Whether a Natural Number Is a Prime -- I. The Sieve of Eratosthenes -- II. Some Fundamental Theorems on Congruences -- III. Classical Primality Tests Based on Congruences -- IV. Lucas Sequences -- V. Primality Tests Based on Lucas Sequences -- VI. Fermat Numbers -- VII. Mersenne Numbers -- VIII. Pseudoprimes -- IX. Carmichael Numbers -- X. Lucas Pseudoprimes -- XL Primality Testing and Large Primes -- XII. Factorization and Public Key Cryptography -- 3 Are There Functions Defining Prime Numbers? -- I. Functions Satisfying Condition (a) -- II. Functions Satisfying Condition (b) -- III. Functions Satisfying Condition (c) -- aNumber theory aDiscrete Mathematics aNumber Theory aDiscrete mathematics2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -2004 uhttps://doi.org/10.1007/978-1-4612-0759-7?nosfx=yxVerlag3Volltext0 a511.1 aThis text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records