Polignac

Polignac is a French surname and the name of a commune in the Haute-Loire department in south-central France. It is also associated with the historical Maison de Polignac, a noble family long prominent in French politics and society. Originating in Poitou, the house produced rulers, diplomats, soldiers, and patrons who held various titles under the Ancien Régime and beyond, and it maintained estates across western and central France.

Polignac, Haute-Loire is a commune in the Auvergne-Rhône-Alpes region. The settlement is known for the Château de Polignac, a medieval fortress perched on a rocky outcrop overlooking the surrounding landscape, which remains a local landmark and tourist site.

In mathematics, Polignac's conjecture is named for the French mathematician Alphonse de Polignac. It asserts that for any even positive integer k there are infinitely many pairs of primes p and p+k. The conjecture generalizes the concept of twin primes. It is a longstanding open problem in number theory; despite progress on related questions about prime gaps, a general proof remains elusive.

The name Polignac continues to appear as a family surname today, and Polignac is used for various places and institutions linked to the historic house and the region.