About: Wolstenholme prime

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In number theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem is a congruence relation satisfied by all prime numbers greater than 3. Wolstenholme primes are named after mathematician Joseph Wolstenholme, who first described this theorem in the 19th century. The only two known Wolstenholme primes are 16843 and 2124679 (sequence in the OEIS). There are no other Wolstenholme primes less than 109.

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rdfs:label	Primo de Wolstenholme (eo) Número primo de Wolstenholme (es) Nombre premier de Wolstenholme (fr) Numero primo di Wolstenholme (it) ウォルステンホルム素数 (ja) Wolstenholme prime (en) Простое число Вольстенхольма (ru)
rdfs:comment	En teoría de números, un número de Wolstenholme es un número primo p si cumple la siguiente condición: Los números de Wolstenholme se nombran en honor a Joseph Wolstenholme (1891-1929), quien demostró el teorema que lleva su nombre, el equivalente a la relación matemática p3 en 1862, siguiendo a Charles Babbage, quien demostró la equivalencia para p2 en 1819. Hasta la fecha, los únicos números primos de Wolstenholme conocidos son 16843 y 2124679 (sucesión A088164 en OEIS); cualquier otro número primo de Wolstenholme debe ser mayor de 109. (es) En mathématiques, un nombre premier p est appelé nombre premier de Wolstenholme si la condition suivante est vérifiée : . Les nombres premiers de Wolstenholme sont nommés en l'honneur du mathématicien Joseph Wolstenholme, qui a démontré en 1862 que tout nombre premier p ≥ 5 vérifie la condition analogue modulo p3 (théorème de Wolstenholme), suite à Charles Babbage qui avait prouvé la condition modulo p2 en 1819. On conjecture qu'il en existe une infinité, bien que les seuls connus soient 16 843 et 2 124 679. et qu'il n'en existe pas d'autres plus petits que 109. (fr) In matematica un numero primo è detto di Primo di Wolstenholme se e solo se Ovvero Gli unici due numeri primi di Wolstenholme attualmente conosciuti sono 16843 e 2124679 (sequenza A088164 dell'OEIS). È stato verificato che non ne esistano altri minori di (it) 数論におけるウォルステンホルム素数（ウォルステンホルムそすう、英: Wolstenholme prime）とは、強い形のを満たすような特別な形をした素数のことである。例えばウォルステンホルムの定理から5以上の素数 p において p−1 までの逆数の和を表す分数の分子は p2 を因数にもつことは知られている。この分数の分子が p3 の因数をもつ素数の事である。名称は19世紀にこの定理を初めて記述した数学者にちなむ。ウォルステンホルム素数への最初の興味が湧き上がったのは、また別の数学的重要性を持つフェルマーの最終定理との関連によってであった。ウォルステンホルム素数は、この定理を一般的に証明すべく研究された、他の特別な数の集合とも関係している。既知のウォルステンホルム素数は、16843 と 2124679 のみである（オンライン整数列大辞典の数列 A088164）。109 以下にはこれ以外にウォルステンホルム素数は存在しない。 (ja) В теории чисел простым числом Вольстенхольма называется всякое простое число, удовлетворяющее усиленному сравнению из теоремы Вольстенхольма. При этом исходному сравнению из теоремы Вольстенхольма удовлетворяют все простые числа, кроме 2 и 3. Простые Вольстенхольма названы в честь математика , который первым доказал теорему в XIX веке. Интерес к этим простым возник по причине их связи с великой теоремой Ферма. Известны только два простых числа Вольстенхольма — это 16843 и 2124679 (последовательность в OEIS). Других простых чисел Вольстенхольма, меньших 109, нет. (ru) En nombroteorio, primo de Wolstenholme estas primo tia ke: La primoj de Wolstenholme estas nomita post Joseph Wolstenholme kiu pruvis la teoremon de Wolstenholme, la ekvivalentan frazon por p3 en 1862, sekve post Charles Babbage montris la ekvivalenton por p2 en 1819. (eo) In number theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem is a congruence relation satisfied by all prime numbers greater than 3. Wolstenholme primes are named after mathematician Joseph Wolstenholme, who first described this theorem in the 19th century. The only two known Wolstenholme primes are 16843 and 2124679 (sequence in the OEIS). There are no other Wolstenholme primes less than 109. (en)
differentFrom	Wolstenholme number
dcterms:subject	Classes of prime numbers Unsolved problems in number theory
Wikipage page ID	29426653 (xsd:integer)
Wikipage revision ID	1104492503 (xsd:integer)
Link from a Wikipage to another Wikipage	Bernoulli number Binomial coefficient Joseph Wolstenholme Paul Zimmermann Congruence relation Empirical relationship Mathematics of Computation Acta Arithmetica Wieferich prime Wilson prime Irregular prime Fermat's Last Theorem Classes of prime numbers Number theory Regular prime Harmonic number Prime number Unsolved problems in number theory Natural logarithm Wolstenholme's theorem Uniform distribution (discrete) Wall–Sun–Sun prime Table of congruences 16843 (number) Left-hand side dbr:2124679_(number)
Link from a Wikipage to an external page	http://www.loria.fr/~zimmerma/records/Wieferich.status http://primes.utm.edu/glossary/xpage/Wolstenholme.html https://books.google.com/books%3Fid=KrA-AAAAYAAJ&pg=PA46 https://books.google.com/books%3Fid=vL0KAAAAIAAJ&pg=PA35 https://web.archive.org/web/20130208001700/http:/imperator.usc.edu/~bruck/research/stirling http://matwbn.icm.edu.pl/ksiazki/aa/aa71/aa7144.pdf%7C http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/padicharmonicsum.pdf http://www.lume.ufrgs.br/bitstream/handle/10183/448/000317407.pdf%3Fsequence=1 http://blms.oxfordjournals.org/content/36/4/553.full.pdf https://www.webcitation.org/5u5TTjyoj%7Cdate=8 https://www.webcitation.org/5uBfEhNBI%7Cdate=12 https://www.webcitation.org/5uBfrPYe8%7Cdate=12 https://www.webcitation.org/5uTrtgMk3%7Cdate=24 https://www.webcitation.org/5uXu6BHu7%7Cdate=27 https://www.webcitation.org/5usC3fNXN%7Cdate=10 https://www.webcitation.org/5usE0UWhy%7Cdate=10 https://www.webcitation.org/5v79AhVZp%7Cdate=20 https://www.webcitation.org/5vRE6GbVK%7Cdate=2 http://www.ams.org/journals/mcom/1975-29-129/S0025-5718-1975-0376606-9/S0025-5718-1975-0376606-9.pdf http://www.ams.org/journals/mcom/1993-61-203/S0025-5718-1993-1197511-5/S0025-5718-1993-1197511-5.pdf http://www.ams.org/mcom/2007-76-260/S0025-5718-07-01955-2/S0025-5718-07-01955-2.pdf%7C http://home.eckerd.edu/~zhaoj/research/ZhaoIJNT.pdf http://home.eckerd.edu/~zhaoj/research/ZhaoJNTBern.pdf%7C
sameAs	Wolstenholme prime Wolstenholme prime Wolstenholme prime Wolstenholme prime Wolstenholme prime Wolstenholme prime Wolstenholme prime Wolstenholme prime Wolstenholme prime

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