Wieferich prime
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's last theorem, at which time both of Fermat's theorems were already well known to mathematicians. As of March 2021, the only known Wieferich primes are 1093 and 3511 (sequence in the OEIS).
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1000 (number)1093 (number)142 (number)241 (number)3000 (number)3511 (number)Abc conjectureArthur WieferichBarker codeCatalan pseudoprimeDmitry MirimanoffDouble Mersenne numberEisenstein reciprocityEuler's theoremFermat numberFermat pseudoprimeFermat quotientGeneralized Wieferich numberGeneralized Wieferich primeHarmonic numberList of distributed computing projectsList of integer sequencesList of number theory topicsList of prime numbersList of unsolved problems in mathematicsLucas-Wieferich primeLucas–Wieferich primeMersenne primeMirimanoff's congruenceN. G. W. H. BeegerNear-Wieferich primeNovember 1909PrimeGridTable of congruencesUnique primeWall–Sun–Sun primeWeiferich primeWieferich's criterionWieferich's theoremWieferich@Home
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Wieferich prime
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's last theorem, at which time both of Fermat's theorems were already well known to mathematicians. As of March 2021, the only known Wieferich primes are 1093 and 3511 (sequence in the OEIS).
has abstract
Eine Wieferich-Primzahl ist ei ...... ieferich erstmals beschrieben.
@de
En matemáticas, un número prim ...... s al último teorema de Fermat.
@es
En mathématiques, un nombre pr ...... au dernier théorème de Fermat.
@fr
Ett Wieferichprimtal är ett pr ...... kända, nämligen 1093 och 3511.
@sv
In matematica, un primo di Wie ...... ti l'ultimo teorema di Fermat.
@it
In number theory, a Wieferich ...... d 3511 (sequence in the OEIS).
@en
Liczba pierwsza Wiefericha – w ...... az 3511 (ciąg A001220 w OEIS).
@pl
Wieferichovo prvočíslo je tako ...... a Wieferichových prvočísel Wn:
@cs
В теории чисел простым числом ...... 1 (последовательность в OEIS).
@ru
若素数，則稱為維費里希素数(Wieferich prime) ...... 是維費里希素数若且唯若，顯然，梅森質數不可能是維費里希素数。
@zh
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Infinite
@en
first terms
10,933,511
largest known term
named after
OEIS
A001220
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publication year
terms number
title
Wieferich prime
@en
urlname
WieferichPrime
@en
wikiPageUsesTemplate
hypernym
comment
Eine Wieferich-Primzahl ist ei ...... ieferich erstmals beschrieben.
@de
En matemáticas, un número prim ...... s al último teorema de Fermat.
@es
En mathématiques, un nombre pr ...... au dernier théorème de Fermat.
@fr
Ett Wieferichprimtal är ett pr ...... kända, nämligen 1093 och 3511.
@sv
In matematica, un primo di Wie ...... ti l'ultimo teorema di Fermat.
@it
In number theory, a Wieferich ...... d 3511 (sequence in the OEIS).
@en
Liczba pierwsza Wiefericha – w ...... az 3511 (ciąg A001220 w OEIS).
@pl
Wieferichovo prvočíslo je tako ...... a Wieferichových prvočísel Wn:
@cs
В теории чисел простым числом ...... 1 (последовательность в OEIS).
@ru
若素数，則稱為維費里希素数(Wieferich prime) ...... 是維費里希素数若且唯若，顯然，梅森質數不可能是維費里希素数。
@zh
label
Liczba pierwsza Wiefericha
@pl
Nombre premier de Wieferich
@fr
Numero primo di Wieferich
@it
Número primo de Wieferich
@es
Wieferich prime
@en
Wieferich-Primzahl
@de
Wieferichovo prvočíslo
@cs
Wieferichprimtal
@sv
Простое число Вифериха
@ru
維費里希素數
@zh