English

Primality tests for 2^kn-1 using elliptic curves

Number Theory 2009-12-31 v1

Abstract

We propose some primality tests for 2^kn-1, where k, n in Z, k>= 2 and n odd. There are several tests depending on how big n is. These tests are proved using properties of elliptic curves. Essentially, the new primality tests are the elliptic curve version of the Lucas-Lehmer-Riesel primality test. Note:An anonymous referee suggested that Benedict H. Gross already proved the same result about a primality test for Mersenne primes using elliptic curve.

Keywords

Cite

@article{arxiv.0912.5279,
  title  = {Primality tests for 2^kn-1 using elliptic curves},
  author = {Yu Tsumura},
  journal= {arXiv preprint arXiv:0912.5279},
  year   = {2009}
}

Comments

8 pages

R2 v1 2026-06-21T14:29:03.367Z