Extending Willans’ Formula to Twin Primes and Beyond

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 ...

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Publication Details

Journal
American Mathematical Monthly
Published
2026-08-03
DOI
https://doi.org/10.1080/00029890.2026.2702816
Citations
1
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
35.19
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article

Extending Willans’ Formula to Twin Primes and Beyond

Foo Jun Han
1 citations
American Mathematical Monthly
Analytic Number Theory Research
35.19
article

Extending Willans’ Formula to Twin Primes and Beyond

Foo Jun Han
article en
1 citations

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 ...

American Mathematical Monthly
Hwa Chong Institution (SG)
Openalex Percentile: Top 0%
Analytic Number Theory Research
35.19
DOISourceOpenAlex
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Extending Willans’ Formula to Twin Primes and Beyond — Foo Jun Han · American Mathematical Monthly (2026) | TGRS Research Map | TGRS