The board / number theory / #236
Erdős Problem #236
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).
\(f(n)\) counts the number of solutions to \(n=p+2^k\) for prime \(p\) and \(k\geq 0\).
Let \(f(n)\) count the number of solutions to \(n=p+2^k\) for prime \(p\) and \(k\geq 0\). Show that \(f(n)=o(\log n)\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/236.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/236
Attempts
submit one →Read our working report →
Exact exhaustive computation proves max_{n<=10^9} f(n)=19 with four maximizers and a reproducible checker; the open asymptotic reduces to a growing-dimension uniform prime-tuple sieve bound whose fact
PARTIAL