Explore the Grid

A pair $(k, n)$ fully determines its Yagel number, so this page computes the exact value in your browser — no server round-trip. Both faces of the grid are available:

$Y_k(n) = p_{k-1}\#\cdot p_k^n - 1$

$Y^{+}_k(n) = p_{k-1}\#\cdot p_k^n + 1$

Here $k$ is the order and $n$ the exponent, $p_k$ is the $k$ -th prime and $p_{k-1}\#$ the primorial of its predecessor. $Y_k(n)$ is the minus face, also called the first kind — order $k=1$ gives the Mersenne numbers — and $Y^{+}_k(n)$ the plus face, the second kind, whose exponent $n=1$ column gives the Euclid numbers $p_k\#+1$ . Primality verdicts are read from the published catalogue of proven primes; see the catalogue and the living paper.

Find a Yagel Number

Order k: Exponent n:

How to read the verdicts

Prime means the exact integer has a deterministic primality proof. The paper states the criteria and hypotheses; a certificate records the witness data checked against the applicable criterion.

Composite means there is evidence for that specific integer: a divisor, or a settled interval of exponents in which every cell was decided and this one came out composite. Unknown means the published data establish no verdict. That happens when the value lies beyond the settled range, or when the only coverage on record is a search reported by an earlier campaign — reported coverage does not by itself decide a value. The value 1 is neither prime nor composite.

This site publishes the catalogue as primes.json and the per-order primality index as index.json. It does not publish the certificate data itself or a complete source archive, and it does not offer an independent verification service. The living paper states the methods and their scope in full.