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Prime Numbers and the Riemann Hypothesis Barry Mazur, William Stein
Publisher: Cambridge University Press

The Riemann Hypothesis is the only problem from Hilbert's list that is also on this new list. PRIME NUMBERS It remains unresolved but, if true, the Riemann Hypothesis will go to the heart of what makes so much of mathematics tick: the prime numbers. Cryptography is a natural application of number theory and so I'd like to write of the Riemann Hypothesis: "Prime numbers behave like a random coin toss. Lots of people know that the Riemann Hypothesis has something to do with prime numbers, but most introductions fail to say what or why. Will the subatomic world help reveal the elusive nature of the primes? In the same year a brief mathematical paper of breathtaking originality was delivered by Bernhard Riemann relating to the distribution of prime numbers. Here we define, then discuss the Riemann hypothesis. Conjecture that has become known as the Riemann Hypothesis. We outline a proof that if the Generalized Riemann Hypothesis holds, then every odd number above 5 is a sum of three prime numbers. This book introduces prime numbers and explains the famous unsolved Riemann hypothesis. Prime numbers are beautiful, mysterious, and beguiling mathematical objects.