Cunningham tables#

This module provides cunningham_prime_factors(), which lists the prime numbers occurring in the factorization of numbers of type \(b^n+1\) or \(b^n-1\) with \(b \in \{2,3,5,6,7,10,11,12\}\). For an introduction to Cunningham prime factors, see Wikipedia article Cunningham_Project. The data becomes available if you install the optional cunningham_tables package by the command

sage -i cunningham_tables

AUTHORS:

  • Yann Laigle-Chapuy (2009-10-18): initial version

sage.databases.cunningham_tables.cunningham_prime_factors()#

List of all the prime numbers occurring in the so called Cunningham table.

They occur in the factorization of numbers of type \(b^n+1\) or \(b^n-1\) with \(b \in \{2,3,5,6,7,10,11,12\}\).

EXAMPLES:

sage: # optional - cunningham_tables
sage: from sage.databases.cunningham_tables import cunningham_prime_factors
sage: cunningham_prime_factors()
[2,
 3,
 5,
 7,
 11,
 13,
 17,
 ...