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erdős #1142

← #1141 · #1143 → (packet.json; erdosproblems.com)

Are there infinitely many $n$ (or any $n > 105$ ) such that $n - 2^{k}$ is prime for all $1 < 2^{k} < n$ ?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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formal

AMS 11 · open (literature)

theorem erdos_1142 :
    answer(sorry) ↔ Infinite { n | Erdos1142Prop n }

formal-conjectures/1142.lean ↗

oeis

A039669 — Numbers n > 2 such that n - 2^k is a prime for all k > 0 with 2^k < n.4,7,15,21,45,75,105

links

the Prime Puzzles website · link

f (n)

count the number of solutions to

n = p + 2^{k}

p

k \geq 0

. Is it true that

f (n) = o (lo g n)

status

open

finding.noted · reviewer:will-blair · 1 day

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