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AuthorRibenboim, Paulo. author
TitleThe New Book of Prime Number Records [electronic resource] / by Paulo Ribenboim
ImprintNew York, NY : Springer New York : Imprint: Springer, 1996
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Descript XXIV, 541 p. online resource


This 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 ยทone.''' 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 apparยญ 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 combinaยญ 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


1 How Many Prime Numbers Are There? -- I. Euclidโ{128}{153}s Proof -- II. Goldbach Did It Too! -- III. Eulerโ{128}{153}s Proof -- IV. Thueโ{128}{153}s Proof -- V. Three Forgotten Proofs -- VI. Washingtonโ{128}{153}s Proof -- VII. Fรผrstenbergโ{128}{153}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) -- IV. 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. Goldbachโ{128}{153}s Famous Conjecture -- VII. The Waring-Goldbach Problem -- VIII. The Distribution of Pseudoprimes, Carmichael Numbers, and Values of Eulerโ{128}{153}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 kร{151}2nยฑ1 -- 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 -- III. Polynomials with Many Successive Composite Values -- IV. Partitio Numerorum -- V. Some Probabilistic Estimates -- Conclusion -- The Pages That Couldnโ{128}{153}t Wait -- Primes up to 10,000 -- Index of Tables -- Index of Names

Mathematics Number theory Discrete mathematics Mathematics Discrete Mathematics Number Theory


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