The New Book of Prime Number RecordsSpringer Science & Business Media, 2012 M12 6 - 541 páginas 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 ˇone.''' 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. |
Contenido
| 1 | |
| 10 | |
Generation of Infinite Sequences of Pairwise Relatively Prime Integers | 17 |
Fermat Numbers | 83 |
Mersenne Numbers | 90 |
Pseudoprimes | 103 |
Strong Lucas Pseudoprimes slpspP Q | 130 |
Factorization and Public Key Cryptography | 162 |
Addendum on kTuples of Primes | 265 |
The Distribution of Pseudoprimes Carmichael Numbers | 311 |
CHAPTER 5 | 323 |
Sophie Germain Primes | 329 |
Primes and SecondOrder Linear Recurrence Sequences | 361 |
CHAPTER 6 | 371 |
The Density of the Set of Regular Primes | 414 |
Conclusion | 427 |
CHAPTER 3 | 177 |
CHAPTER 4 | 213 |
Interlude | 258 |
The Pages That Couldnt Wait | 509 |
| 535 | |
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Términos y frases comunes
a₁ algorithm Amer arithmetic progression b₁ Carmichael numbers Chapter class number Comp composite integers composite numbers congruence conjecture d₁ digits diophantine distinct prime divides divisors Dubner elliptic curves Erdös Euler exist infinitely f₁ f₁(X Fermat numbers Fermat's last theorem gcd(a gcd(N hence infinitely many primes integral coefficients largest known Lehmer Lenstra log log Lucas sequences M₁ Math Mersenne numbers Mersenne primes method mod p˛ multiple n₁ natural number notation number theory odd perfect numbers odd prime p₁ palindromic prime paper polynomial Pomerance positive integers primality tests prime factors prime number theorem prime q prime values primitive prime factor primitive root modulo proof proved quadratic fields regular primes relatively prime result Riemann Riemann's hypothesis satisfied Schinzel Section showed Sierpiński sieve smallest Sophie Germain primes strong pseudoprimes sufficiently large TABLE twin primes Wagstaff Waring's problem
