The New Book of Prime Number Records

Front Cover
Springer Science & Business Media, Dec 6, 2012 - Mathematics - 541 pages
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.
 

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Contents

Introduction
1
Fürstenbergs Proof
10
Generation of Infinite Sequences of Pairwise Relatively Prime Integers
17
The Power of a Prime Dividing a Factorial
30
XII
46
CHAPTER 3
180
Functions Satisfying Condition
186
CHAPTER 4
213
CHAPTER 6
371
The Density of the Set of Regular Primes
414
Conclusion
427
132
457
136
464
153
476
179
488
196
498

Interlude
258
Addendum on kTuples of Primes
265
The WaringGoldbach Problem
299
The Distribution of Pseudoprimes Carmichael Numbers
311
CHAPTER 5
323
Primes and SecondOrder Linear Recurrence Sequences
361
The Pages That Couldnt Wait
509
197
513
203
526
Subject Index
535
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