Home primes (OEIS A037274)

formal-conjectures · oeis · ams-11

Starting from an integer $n\geq 2$, list its prime factors in nondecreasing order with
multiplicity, concatenate their decimal representations, and repeat. The home-prime conjecture
says that this process always reaches a prime.

For example,

$$25 \longmapsto 55 \longmapsto 511 \longmapsto 773.$$

Every integer at least two reaches a home prime.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A037274
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/37274.lean
Local target: Corpus.OEIS37274.home_prime_conjecture
Source SHA-256: 39f11b867ba5e513aaed06a6919052799b5090e1dc7e98a5dfda6802c61a7ba6
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record