Professor tests AIs on an open conjecture — all agree a general proof remains elusive
lemire · x · 2026-08-19
Computer scientist Daniel Lemire posed a conjecture from his own work: for every degree L there exists an irreducible polynomial over GF(2) where every term except x^L has degree less than floor(L/2) — a form that makes Barrett reduction especially cheap. Via Arndt's tables, it holds at least up to L = 400.
He tested various AIs with the conjecture; all agreed that a general proof is still open. Background in his paper "Strongly universal string hashing is fast" (The Computer Journal, 2014).
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