Author | Ribenboim, Paulo. author |
---|---|
Title | The New Book of Prime Number Records [electronic resource] / by Paulo Ribenboim |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0759-7 |
Descript | XXIV, 541 p. online resource |
1 How Many Prime Numbers Are There? -- I. Euclidโs Proof -- II. Goldbach Did It Too! -- III. Eulerโs Proof -- IV. Thueโs Proof -- V. Three Forgotten Proofs -- VI. Washingtonโs Proof -- VII. Fรผrstenbergโs 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. Goldbachโs Famous Conjecture -- VII. The Waring-Goldbach Problem -- VIII. The Distribution of Pseudoprimes, Carmichael Numbers, and Values of Eulerโs 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 kร2nยฑ1 -- 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 Couldnโt Wait -- Primes up to 10,000 -- Index of Tables -- Index of Names