Chapter 18. Formulas For Primes

18–1 Introduction

Like many young students, I once became fascinated with prime numbers and tried to find a formula for them. I didn’t know exactly what operations would be considered valid in a “formula,” or exactly what function I was looking for—a formula for the nth prime in terms of n, or in terms of the previous prime(s), or a formula that produces primes but not all of them, or something else. Nevertheless, in spite of these ambiguities, I would like to discuss a little of what is known about this problem. We will see that (a) there are formulas for primes, and (b) none of them are very satisfying.

Much of this subject relates to the present work in that it deals with formulas similar to those of some of ...

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