Representing Every Prime p ≥ 3 as 2p1 − p2 with Distinct Primes: A Conjecture and Its Computational Verification up to 10^5

We conjecture that every prime p ≥ 3 can be written as p = 2p1 − p2, where p1 and p2 are distinct primes; equivalently, every such prime is an endpoint of a non-constant three-term arithmetic progression of primes. A computer search over all primes p with 3 ≤ p ≤ 10^5 found no exception. The statement remains formally unproved.