Current project record
p₉₉₉# · 7919³⁹¹⁸ + 1
18,664 digits — proven prime by a Pocklington N−1 certificate in 23.5 s. Compute it in your browser →
Every entry below is a proven prime of the form pk−1# · pkn ± 1 — deterministic certificates, not probable-prime claims. The −1 face (first kind) is proven with the Brillhart–Lehmer–Selfridge N+1 test, the +1 face (second kind) with Pocklington's N−1 test; both work because the neighbor of every Yagel number is fully factored by construction. Method, theory, and discovery history are in the living paper.
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| number | k | n | face | digits | certificate | found by |
|---|
Click a number to compute its exact value on the datasets page. Click k / n / digits headers to sort. “Found by”: the 2024 dataset census (k ≤ 50, −1 face), the 2026 mirror census of the +1 face, the 2026 record hunts, the row-opener campaign (first prime of every row through k = 100 and milestones to k = 1000), and the twin companion scan.