World Library  
Flag as Inappropriate
Email this Article

Emirp

Article Id: WHEBN0000526004
Reproduction Date:

Title: Emirp  
Author: World Heritage Encyclopedia
Language: English
Subject: List of prime numbers, Base-dependent integer sequences, 7000 (number), 149 (number), 13 (number)
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Emirp

An emirp (prime spelled backwards) is a prime number that results in a different prime when its digits are reversed.[1] This definition excludes the related palindromic primes. The term reversible prime may be used to mean the same as emirp, but may also, ambiguously, include the palindromic primes.

The sequence of emirps begins 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359,... (sequence A006567 in OEIS).[1]

All non-palindromic permutable primes are emirps.

As of November 2009, the largest known emirp is 1010006+941992101×104999+1, found by Jens Kruse Andersen in October 2007.[2]

The term 'emirpimes' (singular) is used also in places to treat semiprimes in a similar way. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits.

Emirps with added mirror properties

There is a subset of emirps x, with mirror xm, such that x is the yth prime, and xm is the ymth prime. (E.g. 73 is the 21st prime number; its mirror, 37, is the 12th prime number; 12 is the mirror of 21.)

References

  1. ^ a b Weisstein, Eric W., "Emirp", MathWorld.
  2. ^ Rivera, Carlos. "Problems & Puzzles: Puzzle 20.- Reversible Primes". Retrieved on December 17, 2007.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.