Circular prime
Encyclopedia
A circular prime is a prime number
with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime. For example 1193 is a circular prime, since 1931, 9311 and 3119 all are also prime. A circular prime with at least two digits can only consist of combinations of the digits 1, 3, 7 or 9, because having 0, 2, 4, 6 or 8 as the last digit makes the number divisible by 2, and having 0 or 5 as the last digit makes it divisible by 5. The known circular primes are 2, 3, 5, 7, R2, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, R19, R23, R317 and R1031, where Rn is a repunit
prime with n digits. There are no other circular primes up to 1023. Most sources only call the smallest of the primes occurring at the intermediate steps while rotating the digits a circular prime. Another type of primes related to the circular primes are the permutable prime
s, which are a subset of the circular primes (every permutable prime is also a circular prime, but not necessarily vice versa).
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime. For example 1193 is a circular prime, since 1931, 9311 and 3119 all are also prime. A circular prime with at least two digits can only consist of combinations of the digits 1, 3, 7 or 9, because having 0, 2, 4, 6 or 8 as the last digit makes the number divisible by 2, and having 0 or 5 as the last digit makes it divisible by 5. The known circular primes are 2, 3, 5, 7, R2, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, R19, R23, R317 and R1031, where Rn is a repunit
Repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler...
prime with n digits. There are no other circular primes up to 1023. Most sources only call the smallest of the primes occurring at the intermediate steps while rotating the digits a circular prime. Another type of primes related to the circular primes are the permutable prime
Permutable prime
A permutable prime is a prime number, which, in a given base, can have its digits' positions switched through any permutation and still spell a prime number. H. E...
s, which are a subset of the circular primes (every permutable prime is also a circular prime, but not necessarily vice versa).
External links
- Circular prime at The Prime Glossary
- A068652 a related sequence (the circular primes are a subsequence of this one)