Triangular matchstick numbers in the class of prime numbers

formal-conjectures · oeis · ams-11

$a(n) = \sum_{k = n}^{2n} p_k$, where $p_k$ is the $k$-th prime.

Terms are squares at only(?) three values of $n = 3, 6, 4072$:
corresponding terms are 6^2, 13^2, and 15735^2.

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/A105720
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/105720.lean
Local target: Corpus.OEIS105720.conjecture
Source SHA-256: 8dce8d6aa59b1d0116ccc762811c83425876b2f67445d3e2756f127c8255f0ed
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