Alphonse de Polignac (1826–1863) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. In 1849, the year he was admitted to
Polytechnique, he made what's known as
Polignac's conjecture:
[
From p. 400: ''"1er ''Théorème.'' Tout nombre pair est égal à la différence de deux nombres premiers consécutifs d'une infinité de manières … "'' (1st Theorem. Every even number is equal to the difference of two consecutive prime numbers in an infinite number of ways … )]
:For every positive integer ''k'', there are infinitely many
prime gap
A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-th and the
''n''-th prime numbers, i.e.
:g_n = p_ - p_n.\
W ...
s of size 2''k''.
The case ''k'' = 1 is the
twin prime conjecture
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...
.
He also conjectured
Romanov's theorem.
His father,
Jules de Polignac (1780-1847) was prime minister of Charles X until the Bourbon dynasty was overthrown (1830).
See also
*
de Polignac's formula In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime ''p'' that divides the factorial ''n''!. It is named after Adrien-Marie Legendre. It is also sometimes known as de Polignac's formula, aft ...
*
Polignac family
The House of Polignac is the name of an ancient and powerful French noble family that took its name from the '' château de Polignac'', of which they had been ''sieurs'' since Carolingian times. Agnatically, ruling family of Monaco represents ...
References
*
1826 births
1863 deaths
19th-century French mathematicians
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