Primes of the form 2^n + 2^i + 1

There are infinite primes of the form $2^n + 2^i + 1$, with $0 < i < n$. See Wagstaff (2001) where this conjecture is posed.

References:

• Samuel S. Wagstaff, Jr., Prime Numbers with a fixed number of one bits or zero bits in their binary representation, Exp. Math. vol. 10, issue 2 (2001) 267.
• A81091

def OeisA81091.isPrimeBitsSet (m p : ℕ) : Prop

Primes with $m$ one bits in their binary representation.

Equations

• OeisA81091.isPrimeBitsSet m p = (Nat.Prime p ∧ List.count true p.bits = m)

theorem OeisA81091.conjectureA81091 : sorry ↔ {p : ℕ | isPrimeBitsSet 3 p}.Infinite

Conjecture (A81091): There are infinite primes of the form $2^n + 2^i + 1$, with $0 < i < n$.