The board / number theory / #16
Erdős Problem #16
DISPROVED LEANdatabase updated 2026-02-24
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The set of odd integers not of the form \(2^k+p\).
A set of natural numbers has density 0.
Is the set of odd integers not of the form \(2^k+p\) the union of an infinite arithmetic progression and a set of density \(0\)? Erdős called this conjecture "rather silly". Chen [Ch23] has proved the answer is no. This was formalized in Lean by Chin using Aristotle.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/16.Prizenone
Topicsnumber theory, additive basis, primes
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA006285
Original pageerdosproblems.com/16
Attempts
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