Schinzel's hypothesis H

Source placement record

Schinzel's hypothesis H that for every finite collection { f 1 , … , f k } {\displaystyle \{f_{1},\ldots ,f_{k}\}} {\displaystyle \{f_{1},\ldots ,f_{k}\}} of nonconstant irreducible polynomials over the integers with positive leading coefficients, either there are infinitely many positive integers n {\displaystyle n} {\displaystyle n} for which f 1 ( n ) , … , f k ( n ) {\displaystyle f_{1}(n),\ldots ,f_{k}(n)} {\displaystyle f_{1}(n),\ldots ,f_{k}(n)} are all primes, or there is some fixed divisor m > 1 {\displaystyle m>1} {\displaystyle m>1} which, for all n {\displaystyle n} {\displaystyle n}, divides some f i ( n ) {\displaystyle f_{i}(n)} {\displaystyle f_{i}(n)}.

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Source status: Open
Field: Number theory · Prime numbers
Record type: Revision-pinned source placement
Verification: Source-index reviewed
Source grade: secondary
Reviewed: 2026-07-27T18:04:33.834Z

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Source trail

Wikipedia list subsection — Exact Number theory › Prime numbers subsection in the revision-pinned source.
Wikipedia topic article — Background article linked by the source index; follow its references for deeper study.
Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.