Hwa Chong Institution

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 ...