Prime Numbers, Friends Who Give Problems

The following sections are included:

• Dedication
• Preface
• Acknowledgments? Acknowledgments!
• Contents

The following sections are included:

• Multiplication
• Division
• The Euclidean Division Theorem
• The Greatest Common Divisor
• The Least Common Multiple
• Notes About Euclid (circa 300 BCE–circa 279 BCE)

The following sections are included:

• The Sieve
• Notes About Eratosthenes (circa 276 BCE – circa 196 BCE)

The following section is included:

• Notes About Thomas Jan Stieltjes (1856–1894)

The following sections are included:

• Matchbox Cars and Drawers
• Fermat’s Little Theorem
• Notes About Pierre de Fermat (1601–1665)

The following sections are included:

• First Topic: Euler’s Theorem
• Second Topic: The Pairing of Residue Classes
• Third and Last Topic for Today: The Theorem of Wilson
• Notes About Leonhard Euler (1707–1783)

The following sections are included:

• Making Eric Happy
• Patient Paulo’s Turn
• Notes About Adrien-Marie Legendre (1752–1833)

The following section is included:

• Notes About Marin Mersenne (1588–1648)

The following sections are included:

• The Newton Binomial Formula
• Recurring Sequences
• The Proof of the Primality Criterion for Mersenne Numbers
• Notes About Leonardo Pisano, known as Fibonacci (circa 1170–1250)
• Notes About François Edouard Anatole Lucas (1842–1891)
• Notes About Pythagoras of Samos (circa 569 BCE–circa 475 BCE)
• Notes About Blaise Pascal (1623–1662)

The following sections are included:

• Money
• Am I a Good Guy?
• Titanic Primes and Megaprimes
• Curious Primes

The following section is included:

• Public Key Cryptography

The following sections are included:

• New Numbers
• Functions
• The Evaluation of Areas
• Three Functions

The following sections are included:

• Primes up to 10 000
• The Tasks
• Notes About Karl Friedrich Gauss (1777–1855)
• Notes About Johann Martin Zacharias Dase (1824–1861)

The following sections are included:

• Series
• Complex Numbers
• Functions, Limits, Series and All That Stuff

The following sections are included:

• Notes About Pafnuty Lvovich Chebyshev (1821–1894)
• Notes About Georg Friedrich Bernhard Riemann (1826–1866)
• Notes About Charles Jean Gustave Nicolas de la Vallée Poussin (1866–1962)
• Notes About Jacques Salomon Hadamard (1865–1963)
• Notes About Atle Selberg (1917–2007)
• Notes About Pál Erdös (1913–1996)

The following section is included:

• Notes About Johann Peter Gustav Lejeune Dirichlet (1805–1859)

The following sections are included:

• The Riemann Hypothesis
• Twin Primes
• Polignac’s Conjecture
• A Hardy & Littlewood Conjecture
• Curious George
• The Iterated Gaps
• A Letter from Goldbach
• Notes About Christian Goldbach (1690–1764)

The following sections are included:

• The Sophie Germain Primes
• Primes of the Form m² + 1
• Square Arrays of Positive Integers
• Primes in Recurring Sequences
• Repunits
• Notes About Marie Sophie Germain (1776–1831)
• Notes About Viktor Yakovlevich Bunyakovskii (1804–1899)
• Notes About Leonard Eugene Dickson (1874–1954)
• Notes About Wactaw Sierpiński (1882–1969)

The following sections are included:

• The End of the Discussions
• Vacation
• Following the Advice
• Two Weeks Later

The following sections are included:

• Name Index
• Subject Index