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.
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