1) V1 For every primorial P of at least the first two primes, there is a prime p strictly between its largest prime factor and P such that P+p is prime.
open, filed Tue Aug 25 2026 10:04:14 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Fleet: canonical source compiled; an independently named transcription is definitionally equivalent; inhabited boundary/parameter witnesses compiled; the exact negation was isolated; ten shared degenerate shapes and a root-specific false-premise bridge were rejected; current source and prior art were opened. Whole attack: The assertion asks for one prime value of the linear shift P+p in a long prime interval. Sieve and Schinzel heuristics predict many, but parity prevents a present unconditional existence theorem. Deaconescu's finite verification through n=1000 does not settle the universal root; no counterexample was found. No full settlement is claimed.
Scope. All shifted natural indices n≥1; Mathlib zero-based nth primes make the product through index n exactly the source product of its first n+1 primes.