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 for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book Recreations in the Theory of Numbers.[note 1]
A repunit prime is a repunit that is also a prime number. Primes that are repunits in base-2 are Mersenne primes. As of May 2023, the largest known prime number 282,589,933 − 1, the largest probable prime R8177207 and the largest elliptic curve primality-proven prime R86453 are all repunits in various bases.
^Beiler 2013, pp. 83
Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).
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...
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...
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...
199933, 1111111111111111111, 11111111111111111111111 (OEIS: A016114) All repunit primes are circular. A cluster prime is a prime p such that every even...
641, 2137, 3011, 268207, ... (sequence A001562 in the OEIS). See Repunit#Repunit primes for the list of the generalized Wagstaff primes base b {\displaystyle...
from all known cycles of circular primes (The single-digit primes and repunits are the only members of their respective cycles) is 2, 3, 5, 7, R2, 13...
imaginary quadratic field with unique factorization is also 11 (and the first repunit prime in decimal, a base in-which five is also the first non-trivial 1-automorphic...
copies of the digit or group of digits before the subscript. Further down, repunit prime R 317 {\displaystyle R_{317}} is the 29th unique prime, and R 1031...
Global Information