Numbers of the form k*2n 1

Considering odd numbers in the form k*2n 1, known as Robinson numbers

All odd primes can be represented in the form k*2n 1 where k is odd.

Some of the most recent articles are:

17/12/2012 - Thorough updating of search for Keller Primes for k < 106 and survey report

21/04/2007 -In Depth investigation into Keller cycles and their properties

11/04/2005 - Enumeration of Proth primes - now complete for k < 100000 and n 10000.

10/10/2004 - Update to Sierpinski search main article & status report

11/09/2004 - YES I'M BACK! - see the Coming Soon for what I'm currently working on

The following articles cover a variety of interesting issues that I have investigated over the years.

  1. Definitions and background theory - highly recommended
  2. Sierpinski Problem to k < 105 - old
  3. Sierpinski Problem - concentrating on definition and the range 78557 < k < 105 - superseded by the following
  4. Sierpinski Problem to k < 106 - last updated : 10/10/2004, with accompanying Status report
  5. Searching for Robinson primes amongst k < 106 with low Nash weight - ongoing - last updated : 24/05/2002
  6. Searching for larger k with very low Nash weight - ongoing - last updated : 14/02/2000
  7. Searching for Sierpinski numbers - see newer article 15
  8. Covering sets for Sierpinski numbers
  9. Cunningham chains of Robinson primes
  10. Generating large k with very high Nash weight - ongoing - last updated : 30/04/2001
  11. Counting Robinson primes and testing as divisors of generalised Fermat numbers - ongoing - 27/12/2001
  12. Investigation into how surviving Trial Division increases the likelihood that a number is prime - 12/04/2001
  13. Brier Numbers (that is, numbers that are both Sierpinski and Riesel) - 12/04/2001
  14. Prime-Producing Polynomials - 12/04/2001
  15. Extended search for Sierpinski numbers to 2*109 - 30/03/2002
  16. Generalised Cunningham chains - 06/04/2003
  17. Sierpinski Search to k < 107 - last updated 09/01/2004
  18. Enumeration of Proth primes for k < 100000 and n 10000 last updated 11/04/2005.
  19. Keller cycles last updated 03/11/2006.

And don't forget : All you wanted to know about primes

Although there has been little change to the website, there are a number of things I've been working on. These include:

  1. Generalised Fermat divisors - extension
  2. Keller prime search - extension to 10 million

Please send comments and suggestions to : nassarawa at the domain btinternet with a dot com after it.

Last updated : 03/05/2013