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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-28
DOI
https://doi.org/10.5281/zenodo.23017910
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

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

Mohammad Mudassir
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

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

Mohammad Mudassir
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Representing Every Prime p ≥ 3 as 2p1 − p2 with Distinct Primes: A Conjecture and Its Computational Verification up to 10^5 — Mohammad Mudassir · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS