Editing Lucas number (section)

== Lucas primes ==

A '''Lucas prime''' is a Lucas number that is [[prime number|prime]]. The first few Lucas primes are
:2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, ... {{OEIS|id=A005479}}.

The indices of these primes are (for example, ''L''<sub>4</sub> = 7)
:0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, ... {{OEIS|id=A001606}}.
{{as of|2015|09}}, the largest confirmed Lucas prime is ''L''<sub>148091</sub>, which has 30950 decimal digits.<ref>{{cite web |title=The Top Twenty: Lucas Number |url=https://primes.utm.edu/top20/page.php?id=48 |website=primes.utm.edu |access-date=6 January 2022}}</ref> {{as of|2022|08}}, the largest known Lucas [[probable prime]] is ''L''<sub>5466311</sub>, with 1,142,392 decimal digits.<ref>{{cite web |title=Henri & Renaud Lifchitz's PRP Top - Search by form |url=http://www.primenumbers.net/prptop/searchform.php?form=L%28n%29&action=Search |website=www.primenumbers.net |access-date=6 January 2022}}</ref>

If ''L<sub>n</sub>'' is prime then ''n'' is 0, prime, or a [[power of 2]].<ref>Chris Caldwell, "[http://primes.utm.edu/glossary/page.php?sort=LucasPrime The Prime Glossary: Lucas prime]" from The [[Prime Pages]].</ref> ''L''<sub>2<sup>''m''</sup></sub> is prime for ''m''&nbsp;= 1,&nbsp;2,&nbsp;3,&nbsp;and&nbsp;4 and no other known values of&nbsp;''m''.