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Erdős problem #723

If there is a finite projective plane of order $n$ then must $n$ be a prime power? A finite projective plane of order $n$ is a collection of subsets of $\{1,\ldots,n^2+n+1\}$ of size $n+1$ such that every pair of elements is contained in exactly one set.

Why this problem

Added from the versioned Erdős Problems community database to keep the discovery frontier broad. The first pass must validate the exact statement, status, literature, and a concrete verification contract.

Verification contract

Official database status is falsifiable; refine the exact certificate contract before any candidate claim.

Tracking
Difficulty
7/10
Attempts
0
Last attempt
Not yet
Source status
falsifiable
External validation
none
Techniques and harnesses
combinatorics
Resumable campaign memory

Research map

0 epochs · 0 promising · 0 blocked · 0 ruled out
Next session checkpoint

Select the cheapest new discriminator.

First action: Review the source and strategy registry.

Stop or redirect when: The planned discriminator resolves the route.

Open leads
  • No open lead is checkpointed.
Strategy registry
  • No strategy has completed an epoch yet.
Ruled out, with scope
  • Nothing has been rigorously ruled out yet.
Complete history

Attempts on this problem

No attempt has completed yet. The problem is queued transparently.