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140122  eng 
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a 9781461207597

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1 

a Ribenboim, Paulo

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a The New Book of Prime Number Records
h Elektronische Ressource
c by Paulo Ribenboim

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a 3rd ed. 1996

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a New York, NY
b Springer New York
c 1996, 1996

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a XXIV, 541 p
b online resource

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a III. 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 Names

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a IV. PrimeProducing 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 kTuples of Primes  IV. Primes in Arithmetic Progression  V. Primes in Special Sequences  VI. Goldbach’s Famous Conjecture  VII. The WaringGoldbach 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 SecondOrder 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 

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a 1 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) 

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a Number theory

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a Discrete Mathematics

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a Number Theory

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a Discrete mathematics

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a SpringerLink (Online service)

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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u https://doi.org/10.1007/9781461207597?nosfx=y
x Verlag
3 Volltext

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a 511.1

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a 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 ·one.''' He added that the most boring 800page 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
