Schinzel's hypothesis H

proper noun

A famous open problem in mathematics, the hypothesis stating that, for every finite collection f_1,f_2,…,f_k of non-constant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds: (i) there are infinitely many positive integers n such that all of f_1(n),f_2(n),…,f_k(n) are simultaneously prime numbers, or (ii) there is an integer m>1 (called a fixed divisor) which always divides the product f_1(n)f_2(n)⋯f_k(n).

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Meanings

proper noun
  1. mathematicsA famous open problem in mathematics, the hypothesis stating that, for every finite collection f_1,f_2,…,f_k of non-constant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds: (i) there are infinitely many positive integers n such that all of f_1(n),f_2(n),…,f_k(n) are simultaneously prime numbers, or (ii) there is an integer m>1 (called a fixed divisor) which always divides the product f_1(n)f_2(n)⋯f_k(n).

Origin

Named after Andrzej Schinzel.

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Cite this entry
APA

Schinzel's hypothesis H. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Schinzel's%20hypothesis%20H

MLA

“Schinzel's hypothesis H.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Schinzel's%20hypothesis%20H. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Schinzel's hypothesis H,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Schinzel's%20hypothesis%20H.

Source: Schinzel's hypothesis H on Wiktionary, CC BY-SA 4.0.