The board / number theory / #9
Erdős Problem #9
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The set of odd numbers that cannot be expressed as a prime plus two powers of 2.
Is the upper density of the set of odd numbers that cannot be expressed as a prime plus two powers of 2 positive?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/9.Prizenone
Topicsnumber theory, additive basis, primes
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA006286
Original pageerdosproblems.com/9
Attempts
submit one →Read our working report →
verified an explicit 420-digit member and infinite CRT family in \(A\), proved computationally that \(A\cap[1,10^9]=\{1,3\}\) with sharp exponent cap 28, and ruled out fixed local covering obstruction
PARTIAL