The upper-bound conjecture for the Ova-Ova-Prime-Ova construction

From papers

Let the preceding Ova-Ova-Prime-Ova construction be given, and let $N$ denote the number of primes it produces. The Ova-Ova-Prime-Ova counting conjecture. Although the preceding theorem guarantees at least one resulting prime, one has $N\leq 10$ . The source supplies examples and asserts this as a bound, but gives no independent resolution evidence.

Progress summary

Open

No public proof or disproof of the ten-output limit was found, so the conjecture remains open.

The conjecture asserts that the construction produces no more than ten primes. The only related source located describes the construction and its guarantee of at least one output, but does not address this upper bound.

Known results

A 2021 preprint establishes the existence of at least one prime representation for the relevant even inputs, without proving or refuting the bound $N\le 10$ .

Current status (as of August 2026): The at-least-one-output result is recorded, but the upper-bound conjecture $N\le 10$ remains open with no publicly documented proof or counterexample.

Sources

arxiv.org

Sources & referencesView supporting material

Primary source

Yeisson Alexis Acevedo Agudelo, “Prime numbers. An alternative study using ova-angular rotations”, arXiv:2104.04522 (2021).

elementary-number-theory prime-numbers

1 week ago

Take the primes

\rho_1=677=317+360\cdot1, \qquad \rho_2=401=41+360\cdot1.

Their residues are $k_{\rho_1}=317$ and $k_{\rho_2}=41$ , and both rotation frequencies are $1$ . Thus a residue $r$ contributes an output of the prescribed construction precisely when

\gcd(r,360)=1,\qquad k_{\rho_1}+k_{\rho_2}+2-r=360-r\ \text{is prime}, \qquad r+360(1+1)=720+r\ \text{is prime}.

The following $38$ distinct residues satisfy all three conditions:

\begin{aligned} r\in\{& 7,13,23,49,53,67,77,89,91,103,109,119,133,137,161,163,167,187,209,\\ &221,233,247,251,257,263,271,277,289,293,299,301,313,319,329,331,341,343,349 \}. \end{aligned}

For example, the first eleven give

\begin{array}{c|c|c} r&360-r&720+r\\hline 7&353&727\\ 13&347&733\\ 23&337&743\\ 49&311&769\\ 53&307&773\\ 67&293&787\\ 77&283&797\\ 89&271&809\\ 91&269&811\\ 103&257&823\\ 109&251&829 \end{array}

and every entry in the last two columns is prime.

Consequently this single pair of input primes produces $N=38$ prime outputs, contradicting the stated bound $N\le10$ . The earlier published version of the construction proposed the weaker bound $N\le13$ ; the same example disproves that original bound as well.

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Shivam Patel · 1 day ago