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Prime Numbers, Friends Who Give Problems: A Trialogue with Papa Paulo

Paulo Ribenboim
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Megan Patnott
, on

Prime Numbers, Friends Who Give Problems is a charming book, written as a conversation between mathematician Papa Paulo and his grandsons. Papa Paulo begins their conversation by defining prime numbers, and works up to well-known conjectures such as the Twin Primes Conjecture. Along the way, he gives an overview of what is known about prime numbers, including tests for primality, the use of primes in cryptography, the Prime Number Theorem, and the search for ever-larger prime numbers. The book also includes brief biographies of some of the mathematicians whose work on prime numbers is discussed in the conversations.

Ribenboim doesn’t shy away from including proofs and fairly technical computations, so a reader does need to have some mathematics background (at the level of an advanced high school student or beginning math major) and a strong interest in mathematics to enjoy the book. The conversation format lessens the intimidation-factor of the early proofs, since Papa Paulo and his grandsons develop them through discussion. Throughout the book, Papa Paulo encourages his young conversation partners to ask questions and think for themselves. A motivated reader can learn not only about prime numbers, but also something about how mathematicians think, work, and ask questions from reading this book.

Megan Patnott is an Assistant Professor of Mathematics at Regis University in Denver, CO. Her training is in algebraic geometry and commutative algebra.

  • What are Prime Numbers?
  • The Euclidean Division Theorem
  • Another Paulo! The Eratosthenes Sieve
  • How Natural Numbers are Made Out of Primes
  • Tell Me Which is the Largest Prime
  • Trying Hard to Find Primes
  • A Formula, a Formula, Please
  • How to Catch a Prime
  • Beautiful Old Elementary Arithmetic
  • The Old Man Still Knows
  • Can You Tell Me All About Congruences?
  • Homework Checked
  • Testing for Primality and Factorization
  • Fermat Numbers are Friendly. Are They Primes?
  • This World is Perfect
  • Unfriendly Numbers from a Friend of Fermat
  • Paying My Debt
  • Money and Primes
  • Secret Messages
  • New Numbers and Functions
  • Princeps Gauss
  • Gathering Forces
  • The After "Math" of Gauss
  • Primes After Dinner: Bad Dreams?
  • Primes in Arithmetic Progression
  • Selling Primes
  • The Great Prime Mysteries
  • Mysteries in Sequences: More But Not All
  • The End and the Beginning