Unique prime
In recreational number theory, a unique prime or unique period prime is a certain kind of prime number. A prime p ≠ 2, 5 is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1 / p, is equal to the period length of the reciprocal of q, 1 / q. For example, 3 is the only prime with period 1, 11 is the only prime with period 2, 37 is the only prime with period 3, 101 is the only prime with period 4, so they are unique primes. In contrast, 41 and 271 both have period 5; 7 and 13 both have period 6; 239 and 4649 both have period 7; 73 and 137 both have period 8; 21649 and 513239 both have period 11; 53, 79 and 265371653 all have period 13; 31 and 2906161 both have period 15; 17 and 5882353 both have period 16; 2071723 and 536322235
Wikipage redirect
100,000101 (number)11 (number)151 (number)157 (number)165 (number)20,000260 (number)261 (number)290 (number)37 (number)61 (number)9000 (number)Cyclotomic polynomialLargest known prime numberList of prime numbersList of recreational number theory topicsRepeating decimalSamuel YatesUnique period prime
Link from a Wikipage to another Wikipage
primaryTopic
Unique prime
In recreational number theory, a unique prime or unique period prime is a certain kind of prime number. A prime p ≠ 2, 5 is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1 / p, is equal to the period length of the reciprocal of q, 1 / q. For example, 3 is the only prime with period 1, 11 is the only prime with period 2, 37 is the only prime with period 3, 101 is the only prime with period 4, so they are unique primes. In contrast, 41 and 271 both have period 5; 7 and 13 both have period 6; 239 and 4649 both have period 7; 73 and 137 both have period 8; 21649 and 513239 both have period 11; 53, 79 and 265371653 all have period 13; 31 and 2906161 both have period 15; 17 and 5882353 both have period 16; 2071723 and 536322235
has abstract
In der Unterhaltungsmathematik ...... s im Jahr 1980 von untersucht.
@de
In recreational number theory, ...... n studied in any numeral base.
@en
Un nombre premier différent de ...... la période de 1/p (suite ) :
@fr
В теории чисел Уникальное прос ...... тое число имело 10,081 знаков.
@ru
唯一素数（Unique prime）是指一個不為2, 5，有 ...... 至2010年為止，確定是質數的最大唯一素数有10081位數。
@zh
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,007,435,787
Link from a Wikipage to another Wikipage
con number
Infinite
@en
date
October 2016
@en
first terms
31,137,101
largest known term
/9
@en
OEIS
A040017
@en
OEIS name
Unique period primes in order
@en
reason
what is an overpesudoprime?
@en
terms number
wikiPageUsesTemplate
comment
In der Unterhaltungsmathematik ...... s im Jahr 1980 von untersucht.
@de
In recreational number theory, ...... riod 16; 2071723 and 536322235
@en
Un nombre premier différent de ...... la période de 1/p (suite ) :
@fr
В теории чисел Уникальное прос ...... тное 7 (0.142857142857142857…)
@ru
唯一素数（Unique prime）是指一個不為2, 5，有 ...... 環單位(10270343-1)/9是已知最大的可能唯一素数。
@zh
label
Einzigartige Primzahl
@de
Nombre premier unique
@fr
Unique prime
@en
Уникальное простое
@ru
唯一素数
@zh