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.23017909
Primary Topic
Analytic Number Theory Research
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
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
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

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