Search: id:A003459
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%I A003459 M0658
%S A003459 2,3,5,7,11,13,17,31,37,71,73,79,97,113,131,199,311,337,373,733,
%T A003459 919,991,1111111111111111111,11111111111111111111111
%N A003459 Absolute primes: every permutation of digits is a prime.
%C A003459 "The prime repunits are examples of integers which are prime and remain 
               prime after an arbitrary permutation of their decimal digits. Integers 
               with this property are called either 'permutable primes' according 
               to H.-E. Richert, who introduced them some 40 years ago, or 'absolute 
               primes' according to T. N. Bhagava and P. H. Doyle and A. W. Johnson."
%C A003459 This sequence has no terms with 4, 5 and 6 digits (by exhaustive search). 
               - Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Jun 16 2005
%C A003459 Depending on the source, permutable or absolute primes are sometimes 
               required to have at least two different digits. This produces the 
               subsequence A129338. - Maximilian F. Hasler (www.univ-ag.fr/~mhasler), 
               Mar 26 2008
%D A003459 Angell, I. O. and Godwin, H. J. "On Truncatable Primes." Math. Comput. 
               31, 265-267, 1977.
%D A003459 T. N. Bhargava and P. H. Doyle, On the existence of absolute primes, 
               Math. Mag., 47 (1974), 233.
%D A003459 A. W. Johnson, Absolute primes, Mathematics Magazine, 1977, vol. 50, 
               pp. 100-103.
%D A003459 Rich Schroeppel (rschroe(AT)sandia.gov), personal communication.
%D A003459 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003459 C. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=PermutablePrime">
               The prime glossary: Permutable Prime</a>
%H A003459 J. P. Delahaye, Persistent Primes, <a href="http://www.pour-la-science.com/
               numeros/pls-258/log3.htm">Illustrating Permutable, Circular, Right 
               & Left Truncatable Primes</a>
%H A003459 R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/
               ">The Top Ten: a Catalogue of Primal Configurations</a>
%H A003459 W. Schneider, MATHEWS, <a href="http://www.wschnei.de/digit-related-numbers/
               circular-primes.html">Circular, Permutable, Truncatable and Deletable 
               Primes</a>
%H A003459 A. Slinko, <a href="http://matholymp.com/ARTICLES/Absolute_Primes.pdf">
               Absolute Primes</a>
%H A003459 Wikipedia, <a href="http://en.wikipedia.org/wiki/Permutable_prime">Permutable 
               prime</a>
%H A003459 <a href="Sindx_Tri.html#tprime">Index entries for sequences related to 
               truncatable primes</a>
%Y A003459 Includes all of A004023. Cf. A129338.
%Y A003459 Sequence in context: A107845 A090934 A068652 this_sequence A118725 A117835 
               A120639
%Y A003459 Adjacent sequences: A003456 A003457 A003458 this_sequence A003460 A003461 
               A003462
%K A003459 nonn,base,nice
%O A003459 1,1
%A A003459 N. J. A. Sloane (njas(AT)research.att.com).
%E A003459 The next terms are R(317), R(1031), R(49081), where R(n) is (10^n-1)/
               9.
%E A003459 Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 18 
               2000

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