Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Lucasian Criteria for the Primality of N = h · 2n - 1

Hans Riesel
Mathematics of Computation
Vol. 23, No. 108 (Oct., 1969), pp. 869-875
DOI: 10.2307/2004975
Stable URL: http://www.jstor.org/stable/2004975
Page Count: 7
  • Read Online (Free)
  • Download ($34.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Lucasian Criteria for the Primality of N = h · 2n - 1
Preview not available

Abstract

Let vi = v2i-1 - 2 with v0 given. If $v_{n - 2} \equiv 0 (\operatorname{mod} N)$ is a necessary and sufficient criterion that N = h · 2n - 1 be prime, this is called a Lucasian criterion for the primality of N. Many such criteria are known, but the case h = 3A has not been treated in full generality earlier. A theorem is proved that (by aid of computer) enables the effective determination of suitable numbers v0 for any given N, if $h < 2^n$. The method is used on all N in the domain h = 3(6)105, n ≤ 1000. The Lucasian criteria thus constructed are applied, and all primes N = h · 2n - 1 in the domain are tabulated.

Page Thumbnails

  • Thumbnail: Page 
869
    869
  • Thumbnail: Page 
870
    870
  • Thumbnail: Page 
871
    871
  • Thumbnail: Page 
872
    872
  • Thumbnail: Page 
873
    873
  • Thumbnail: Page 
874
    874
  • Thumbnail: Page 
875
    875