Extending Willans’ Formula to Twin Primes and Beyond
Abstract
61 years ago, Willans proposed an explicit formula for the nth prime, p(n) [1]. Based on Wilson’s theorem—that (p−1)!+1p∈Z iff p is prime or 1—Willans observed that cos 2(πx)=1 when x∈Z, and lies ...
Fields of Study & Subjects
Analytic Number Theory Research
Mathematics and Applications
Advanced Mathematical Identities
Publication details
- Journal / source
- American Mathematical Monthly
- Publisher
- Informa UK Limited
- Pages
- 1–1
- Publication date
- 3 August 2026
- Language
- EN