The New Book of Prime Number Records

1. Front Matter

   Pages i-xxiv

   PDF

2. Introduction

   • Paulo Ribenboim

   Pages 1-2

3. How Many Prime Numbers Are There?

   • Paulo Ribenboim

   Pages 3-18

4. How to Recognize Whether a Natural Number Is a Prime

   • Paulo Ribenboim

   Pages 19-178

5. Are There Functions Defining Prime Numbers?

   • Paulo Ribenboim

   Pages 179-212

6. How Are the Prime Numbers Distributed?

   • Paulo Ribenboim

   Pages 213-322

7. Which Special Kinds of Primes Have Been Considered?

   • Paulo Ribenboim

   Pages 323-369

8. Heuristic and Probabilistic Results about Prime Numbers

   • Paulo Ribenboim

   Pages 371-425

9. Conclusion

   • Paulo Ribenboim

   Pages 427-432

10. Back Matter

    Pages 433-541

    PDF

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 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.

• Graph
• Mersenne number
• Mersenne prime
• Prime
• Prime number
• Sim
• cryptography

Third Edition

P. Ribenboim

The New Book of Prime Number Records

"A number-theoretical version of the Guinness Book of Records . . . There is much mathematics to be found in these pages. These are records given here as well. This book is written with much wit. Experts may not find much that is new, but it is always worthwhile to view the history of a subject as a whole rather than a collection of isolated results."—MATHEMATICAL REVIEWS

• Department of Mathematics and Statistics, Queen’s University, Kingston, Canada

  Paulo Ribenboim

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