Sum of next $n$ primes

formal-conjectures · oeis · ams-11

The sum of the primes in the $n$-th row of the prime number triangle:
$$a(n) = \sum_{i = 1 + n(n-1)/2}^{n + n(n-1)/2} p_i$$
with $a(0) = 0$.

The only positive integer $n$ such that $a(n)$ is a perfect square is $n=38$.
- Carlos Eduardo Olivieri, Mar 09 2015

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/A007468
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/7468.lean
Local target: Corpus.OEIS7468.conjecture
Source SHA-256: 5871251c9a1cdc947e42f7052ef4097b51884b8a2f02bb2ea2baa0364ce6204d
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.

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