For every prime p≥ 3, there exist distinct primes p_1 and p_2 such that p=2p_1-p_2; equivalently, forall p∈P,(p≥ 3 impliesexists p_1,p_2∈P,(p_1≠ p_2 land p=2p_1-p_2)), where P denotes the set of primes.

Representing every prime p ≥ 3 as 2p₁ − p₂ with distinct primes

For every prime $p\ge 3$ , there exist distinct primes $p_1$ and $p_2$ such that $p=2p_1-p_2$ ; equivalently, $\forall p\in\mathbb{P}\,(p\ge 3\implies\exists p_1,p_2\in\mathbb{P}\,(p_1\ne p_2\land p=2p_1-p_2))$ , where $\mathbb{P}$ denotes the set of primes.

References

Primary source

Zenodo (CERN European Organization for Nuclear Research)

Additional references

Representing Every Prime p ≥ 3 as 2p1 − p2 with Distinct Primes: A Conjecture and Its Computational Verification up to 1010 — Zenodo (CERN European Organization for Nuclear Research) — Mohammad Mudassir
Representing Every Prime p ≥ 3 as 2p1 − p2 with Distinct Primes: A Conjecture and Its Computational Verification up to 1010 — Zenodo (CERN European Organization for Nuclear Research) — Mohammad Mudassir

Posted 1 week ago · edited 1 week ago

Progress summary

Refreshed 1 week ago

Claimed progress

A new conjecture says every prime can be built from two distinct primes in a specified way, and a computer has checked it up to ten billion without proving it universally.

The conjecture asks whether every prime $p \ge 3$ can be written as $2p_1-p_2$ , where $p_1$ and $p_2$ are distinct primes.

September 2026 computational check

A Zenodo deposit by Mohammad Mudassir states the conjecture and reports a finite verification for all relevant primes through $10^{10}$ . This is evidence for the conjecture, not a proof of its universal claim.

Current status (as of September 2026): The conjecture is computationally verified through $10^{10}$ , while the universal statement remains open.

Sources

No solutions have been posted yet.