The Best New Prime Numbers Books To Read In 2025

This book presents prime numbers in a beginner-friendly way, offering detailed proofs, definitions, examples, and exercises on key theorems and concepts. Each chapter includes exercises designed to reinforce and practice the concepts of prime numbers. The book introduces prime and composite numbers, covering primality tests and the Sieve of Eratosthenes. It formalizes prime factorization as tuples and presents a straightforward method for finding the prime factorization of integers. The book also explains how to determine the GCD and LCM of a set of numbers using their prime factorizations.

Through detailed examples, we illustrate the Sieve of Eratosthenes for identifying prime numbers. We establish the infinitude of primes with several proofs, including Euclid's famous argument. The book discusses Mersenne and Fermat primes, along with significant conjectures such as the twin prime conjecture, Goldbach's conjecture, and the Mersenne prime conjecture. We also cover primes in arithmetic progression and applications of Dirichlet's theorem. Finally, we explore the distribution of primes using Bertrand's postulate, the prime-counting function, and the prime number theorem. Here are some of the topics you will learn:prime and composite numbersprimality testsieve of Eratosthenesprime factorizationinfinitude of primesMersenne primesFermat primesGoldbach conjecturetwin prime conjectureprime number theoremBertrand's postulate (Chebyshev's theorem).

Prepare yourself for the ultimate number you'll ever need—M136279841, the largest prime ever discovered! This mathematical titan, known as a Mersenne prime, has 41,024,320 digits. It eclipses by more than 16 million digits the previous largest known prime number found by GIMPS nearly 6 years ago. In this special edition, we've printed every single digit of this colossal number. Yes, you read that right. A book packed with nothing but the digits of M136279841. It's part of a rare breed of primes, known as Mersenne primes. It is only the 52nd known Mersenne prime ever discovered, each increasingly more difficult to find.

Thanks to the dedicated volunteers of GIMPS (Great Internet Mersenne Prime Search), which has found the last 18 Mersenne primes, we can bring this prime to you. They’ve even put a cash prize on the line for anyone lucky enough to find the next one! And hey, when civilization collapses (not saying it will, but, you know, just in case), you’ll want this book on hand. Imagine needing a long prime number to reboot society’s encryption algorithms or simply impress future generations with your foresight! Plus, it makes a great conversation starter. Who doesn’t want to own the largest prime number known to humanity? Get your copy today and hold a piece of mathematical history in your hands. (This is volume 2 of 2).

Prepare yourself for the ultimate number you'll ever need—M82589933, the newest and largest prime ever discovered! This mathematical titan, known as a Mersenne prime, is the result of multiplying together 82,589,933 twos and then subtracting one. With over one and a half million more digits than the previous record-holder, it’s a true masterpiece of number theory. In this special edition, we've printed every single digit of this colossal number. Yes, you read that right. A book packed with nothing but the digits of M82589933.

It's part of a rare breed of primes, known as Mersenne primes, named after the French monk Marin Mersenne, who was fascinated by these mystical numbers over 350 years ago. Thanks to the dedicated volunteers of GIMPS (Great Internet Mersenne Prime Search), which has found the last 17 Mersenne primes, we can bring this prime to you. They’ve even put a cash prize on the line for anyone lucky enough to find the next one! And hey, when civilization collapses (not saying it will, but, you know, just in case), you’ll want this book on hand. Imagine needing a long prime number to reboot society’s encryption algorithms or simply impress the future generations with your foresight! Plus, it makes a great conversation starter. Who doesn’t want to own the largest prime number known to humanity? Get your copy today and hold a piece of mathematical history in your hands.