In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands...

This is a list of repunit primes in various bases. Base-2 repunit primes are called Mersenne primes. The first few base-3 repunit primes are 13, 1093...

repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which...

199933, 1111111111111111111, 11111111111111111111111 (OEIS: A016114) All repunit primes are circular. A cluster prime is a prime p such that every even...

11111111111111111111111, ... (sequence A004022 in the OEIS). These primes are called repunit primes. Another example is when we take b = −12, we get n values of: 2...

faulty. Repunits are integers that are represented with only the digit 1. For example, 1111 (one thousand, one hundred and eleven) is a repunit. Repdigits...

squaring the square). 111 is R 3 {\displaystyle R_{3}} or the second repunit in decimal, a number like 11, 111, or 1111 that consists of repeated units...

051 = fifth Keith prime 1,089,270 = harmonic divisor number 1,111,111 = repunit 1,112,083 = logarithmic number 1,129,30832 + 1 is prime 1,136,689 = Pell...

primes, but later they were also called absolute primes. In base 2, only repunits can be permutable primes, because any 0 permuted to the ones place results...

in decimal R 19 {\displaystyle R_{19}} is also the second to be a prime repunit (after R 2 {\displaystyle R_{2}} ), followed by R 23 {\displaystyle R_{23}}...

641, 2137, 3011, 268207, ... (sequence A001562 in the OEIS). See Repunit#Repunit primes for the list of the generalized Wagstaff primes base b {\displaystyle...

Sierpinski problem 55555 = repdigit 55860 = harmonic divisor number 55987 = repunit prime in base 6 56011 = Wedderburn-Etherington number 56092 = the number...

Eisenstein integers. 271 is the largest prime factor of the five-digit repunit 11111, and the largest prime number for which the decimal period of its...

is a square (11 times 11) the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form 1 + p + p 2...

divisible by the sum of its digits, making it a Harshad number. The smallest repunit probable prime in base 152 was found in June 2015, it has 589570 digits...

a repunit, a number consisting only of n ones (in base 10). There are no other circular primes up to 1025. The only other known examples are repunit primes...

2002 TK102 Repeated 1 1 Ceres 11 Parthenope 111 Ate 1111 Reinmuthia 11111 Repunit (111111) 2001 VO84 Repeated 2 2 Pallas 22 Kalliope 222 Lucia 2222 Lermontov...

number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 319 = 11 × 29. 319 is the sum of three consecutive primes (103 +...

palindromic prime in 2 consecutive bases: 23 (KLK23) and 24 (J5J24) 11111 = Repunit 11297 = Number of planar partitions of 16 11298 = Riordan number 11311...

Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit Repunit Self-descriptive Smarandache–Wellin Undulating Digit-permutation related...

972,410,221 = number of trees with 32 unlabeled nodes 111,111,111,111 = repunit 118,587,876,497 = 49133 = 179 127,004,500,762 = number of parallelogram...

1038232 = 22093 = 476 11,019,960,576 = 1049762 = 3244 = 188 11,111,111,111 = repunit 11,123,060,678 = number of free 21-ominoes 11,874,568,703 = number of partitions...

(sequence A059754 in the OEIS). Smith numbers can be constructed from factored repunits.[verification needed] As of 2010[update], the largest known Smith number...

the smallest prime congruent to 1 modulo 24, as well as the only prime repunit in octal (1118). It is the fourth star number. Where 73 and 37 are part...

number of partially ordered set with 12 unlabeled elements 1,111,111,111 : repunit, also a special number relating to the passing of Unix time. 1,129,760...

concept, professional mathematicians generally are not. Like the concept of repunits and palindromic numbers, the concept of strobogrammatic numbers is base-dependent...

with 10,000 or more decimal digits.[citation needed] He is the author of Repunits and Repetends. Between 1940 and 1973 Yates worked a number of different...

Demlo numbers 1, 121, 12321, 1234321, ..., which are the squares of the repunits 1, 11, 111,1111, .... Prahalad Chunnilal Vaidya "क्‍या आप जानते हैं जादुई...

power and not of the form −4k4 for integer k, are there infinitely many repunit primes to base b? For any given integers k ≥ 1 , b ≥ 2 , c ≠ 0 {\displaystyle...

integer ≥ 2 for z, this sum becomes a base z repunit. Thus a necessary (but not sufficient) condition for a repunit to be prime is that its length be prime...