Circular prime

Circular prime
Circular prime
Named after Circle
Publication year 2004
Author of publication Darling, D. J.
Number of known terms 23
First terms 2, 3, 5, 7, 11, 13
Largest known term R1031
OEIS index A016114

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.[1][2] For example 1193 is a circular prime, since 1931, 9311 and 3119 all are also prime.[3] 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.[1][4] 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.[3] 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 primes, which are a subset of the circular primes (every permutable prime is also a circular prime, but not necessarily vice versa).[3]

References

  1. ^ a b The Universal Book of Mathematics, Darling, David J., http://books.google.de/books?id=nnpChqstvg0C&pg=PA70&dq=circular+prime&hl=de&ei=4TVMTLTOMYSD4Qag-MSaDA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDcQ6AEwAw#v=onepage&q=circular%20prime&f=false, retrieved 25 July 2010 (see page 70) 
  2. ^ Prime Numbers - The Most Mysterious Figures in Math, Wells, D., http://wenku.baidu.com/view/8d95d909581b6bd97f19ea85.html, retrieved 27 July 2010 (see page 47 (page 28 of the book)) 
  3. ^ a b c Circular Primes, Patrick De Geest, http://www.worldofnumbers.com/circular.htm, retrieved 25 July 2010 
  4. ^ The mathematics of Oz: mental gymnastics from beyond the edge, Pickover, Clifford A., http://books.google.de/books?id=4qA2qZhVb9AC&pg=PA330&dq=circular+prime&hl=de&ei=NaB3TYzZE8vAtAb72NH7BA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDgQ6AEwAQ#v=onepage&q=circular%20prime&f=false, retrieved 9 March 2011 (see page 330) 

External links

  • Circular prime at The Prime Glossary
  • A068652 a related sequence (the circular primes are a subsequence of this one)

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