World Library  
Flag as Inappropriate
Email this Article


Article Id: WHEBN0013398615
Reproduction Date:

Title: Super-prime  
Author: World Heritage Encyclopedia
Language: English
Subject: Prime number
Publisher: World Heritage Encyclopedia


For the computer program, see SuperPrime.

Super-prime numbers (also known as "higher order primes") are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins

3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, … (sequence OEIS).

That is, if p(i) denotes the ith prime number, the numbers in this sequence are those of the form p(p(i)). Dressler & Parker (1975) used a computer-aided proof (based on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers. Their proof relies on a result resembling Bertrand's postulate, stating that (after the larger gap between super-primes 5 and 11) each super-prime number is less than twice its predecessor in the sequence.

Broughan and Barnett[1] show that there are

\frac{x}{(\log x)^2}+O\left(\frac{x\log\log x}{(\log x)^3}\right)

super-primes up to x. This can be used to show that the set of all super-primes is small.

One can also define "higher-order" primeness much the same way, and obtain analogous sequences of primes. Fernandez (1999)

A variation on this theme is the sequence of prime numbers with palindromic indices, beginning with

3, 5, 11, 17, 31, 547, 739, 877, 1087, 1153, 2081, 2381, … (sequence OEIS).


  • .
  • .

External links

  • A Russian programming contest problem related to the work of Dressler and Parker
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, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for 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.