Mathematicians
Alphonse de Polignac
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French mathematician who worked in number theory. In 1849 he proposed what is now called de Polignac's conjecture: for every positive even number 2k, there are infinitely many pairs of consecutive primes differing by exactly 2k. The case k equals 1, a gap of exactly two, is the twin prime conjecture; Polignac's statement is the broader family of conjectures of which it is the best-known member. Like the twin prime conjecture itself, de Polignac's conjecture in its general form remains unproven.
Facts
Birth YearYear-only precision per English Wikipedia; Wikidata gives an unsourced exact date of 27 March 1826, not used here for lack of a primary citation. Death YearYear-only precision; one secondary aggregator (PeoplePill) gives 1862 instead, a minor cross-source conflict not resolved by a primary record. Nationality / Culture Defining ContributionFirst clearly posed, in 1849, the general conjecture that every positive even number occurs infinitely often as the gap between consecutive primes; the twin prime conjecture is the smallest-gap special case of this broader statement. 2 Notable WorkFormulated de Polignac's conjecture (1849): for every positive even number 2k, there are infinitely many pairs of consecutive primes differing by exactly 2k. 1 Cross-Tradition Connections
Conjectures Posed
First clearly posed the modern form in 1849, as the k=1 case of his own broader conjecture about fixed prime gaps.
In Branch
Sources
1. Alphonse de Polignac (Wikipedia)
Wikimedia Foundationopening paragraphQuote, opening paragraph
Alphonse de Polignac (1826-1863) was a French mathematician and aristocrat.
1. Alphonse de Polignac (Wikipedia)
Wikimedia Foundationearly-life textQuote, early-life text
Alphonse was born in London during his father's time as ambassador to the United Kingdom.
1. Alphonse de Polignac (Wikipedia)
Wikimedia FoundationNumber theory sectionQuote, Number theory section
For every positive integer k, there are infinitely many prime gaps of size 2k
2. Wolfram MathWorld
Wolfram Research, Inc.
Wikipedia: Twin Prime
Wikimedia FoundationConjectures Posed: Twin Prime Conjecture, Twin prime conjecture sectionQuote, Conjectures Posed: Twin Prime Conjecture, Twin prime conjecture section
In 1849, de Polignac made the more general conjecture that for every natural number k, there are infinitely many primes p such that p + 2k is also prime. The case k = 1 of de Polignac's conjecture is the twin prime conjecture.
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