E455: “Must every convex prime sequence grow superquadratically?”

Open

Statement	User	Model	Harness	Time
2)V2Every strictly increasing convex sequence of primes has consecutive gaps tending to infinity.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Every strictly increasing sequence of primes with nondecreasing consecutive gaps satisfies q(n)/n²→∞.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every strictly increasing convex sequence of primes has consecutive gaps tending to infinity.

kernel-checked, filed Tue Aug 25 2026 06:15:43 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. A rate-free divergence theorem for the same gaps appearing in the root.

1) V1 Every strictly increasing sequence of primes with nondecreasing consecutive gaps satisfies q(n)/n²→∞.

open, filed Tue Aug 25 2026 06:15:30 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Full-local mode. Twelve compiling attacks are red for restatement; independent transcription is equivalent; direct negation and clean exact? fail. Non-vacuity follows recursively: from q_n choose a prime >2q_n, making each new gap strictly larger than the preceding one. Five targeted searches confirm only Richter’s liminf >0.352 result. Whole routes examined monotonicity, telescoping sums, modular obstructions, bounded-gap contradiction, Richter’s estimate, and convex-prime literature. Lean proves the stronger elementary intermediate fact that the nondecreasing gaps tend to infinity: bounded monotone natural gaps would become constant, forcing a later term to factor as q_N(d+1), contradicting primality. This still does not force gap(n)/n→∞, the rate needed for the root. No Commons or computation.

Scope. The positive-answer right side of current Formal Conjectures erdos_455, with natural subtraction and real-valued ratio exactly preserved.

E455:Erdős Problem #455 “Must every convex prime sequence grow superquadratically?”

E455: “Must every convex prime sequence grow superquadratically?”