A Proof of the Lucas-Lehmer Test and its Variations by Using a Singular Cubic Curve


KÜÇÜKSAKALLI Ö.

JOURNAL OF INTEGER SEQUENCES, vol.21, no.6, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 6
  • Publication Date: 2018
  • Journal Name: JOURNAL OF INTEGER SEQUENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Middle East Technical University Affiliated: Yes

Abstract

We give another proof of the Lucas-Lehmer test by using a singular cubic curve. We also illustrate a practical way to choose a starting term for the Lucas-Lehmer-Riesel test by trial and error. Moreover, we provide a nondeterministic test for determining the primality of integers of the form N = hp(n) - 1 for any odd prime p. We achieve these by using the group structure on a singular cubic curve induced from the group law of elliptic curves.