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Difference between revisions of "Cullen number"
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{{V|C<sub>n</sub>}} is [[prime]] for {{Vn}} = 1, 141, {{PP|40087|4713}}, {{PP|38112|5795}}, {{PP|37374|6611}}, {{PP|23436|18496}}, {{PP|17877|32292}}, {{PP|17850|32469}}, {{PP|10752|59656}}, {{PP|5931|90825}}, {{PP|271|262419}}, {{PP|102|361275}}, {{PP|77|481899}}, {{PP|75433|1354828}}, {{PP|87775|6328548}}, {{PP|89536|6679881}} and for no other {{Vn}} < {{Num|{{GP|Cullen prime 2|CuMaxn}}}} ({{OEIS|l|A005849}}). | {{V|C<sub>n</sub>}} is [[prime]] for {{Vn}} = 1, 141, {{PP|40087|4713}}, {{PP|38112|5795}}, {{PP|37374|6611}}, {{PP|23436|18496}}, {{PP|17877|32292}}, {{PP|17850|32469}}, {{PP|10752|59656}}, {{PP|5931|90825}}, {{PP|271|262419}}, {{PP|102|361275}}, {{PP|77|481899}}, {{PP|75433|1354828}}, {{PP|87775|6328548}}, {{PP|89536|6679881}} and for no other {{Vn}} < {{Num|{{GP|Cullen prime 2|CuMaxn}}}} ({{OEIS|l|A005849}}). | ||
| − | The largest known Cullen prime is {{PP|89536|{{Kbn|+|6679881|6679881}}}} and the largest known generalized Cullen prime is {{PP| | + | The largest known Cullen prime is {{PP|89536|{{Kbn|+|6679881|6679881}}}} and the largest known generalized Cullen prime is {{PP|132658|{{Kbn|+|2525532|73|2525532}}}}. |
==Current status== | ==Current status== | ||
| Line 16: | Line 16: | ||
==External links== | ==External links== | ||
| − | *[ | + | *[https://t5k.org/top20/page.php?id=6 Top 20 Cullen Primes] |
| − | *[ | + | *[https://t5k.org/top20/page.php?id=42 Top 20 Generalized Cullen Primes] |
| − | *[http://yves.gallot.pagesperso-orange.fr/primes/chrrcds.html#Cullen The Chronology of Prime Number Records] | + | *[https://web.archive.org/web/20231002091553/http://yves.gallot.pagesperso-orange.fr/primes/chrrcds.html#Cullen Web archive of The Chronology of Prime Number Records] |
*[http://web.archive.org/web/20161022062919/http://www.prothsearch.net:80/cullen.html Web archive "prothsearch.net"] | *[http://web.archive.org/web/20161022062919/http://www.prothsearch.net:80/cullen.html Web archive "prothsearch.net"] | ||
*[http://www.loeh.name/guenter/gc/status.html Generalized Cullen Search, Günter Löh (3 ≤ base ≤ 100), dated Sept. 2017] | *[http://www.loeh.name/guenter/gc/status.html Generalized Cullen Search, Günter Löh (3 ≤ base ≤ 100), dated Sept. 2017] | ||
| Line 25: | Line 25: | ||
*[[Wikipedia:Cullen_number|Cullen number]] | *[[Wikipedia:Cullen_number|Cullen number]] | ||
*[http://mathworld.wolfram.com/CullenNumber.html Mathworld] | *[http://mathworld.wolfram.com/CullenNumber.html Mathworld] | ||
| − | *[http:// | + | *[http://t5k.org/glossary/xpage/Cullens.html The Prime Glossary] |
[[Category:Number]] | [[Category:Number]] | ||
Latest revision as of 04:57, 5 March 2025
A Cullen number Cn is a number of the form n•2n+1,
a generalized Cullen number base b is a number of the form n•bn+1. (perhaps own page?)
Cullen primes
Cn is prime for n = 1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881 and for no other n < 26,000,000 (sequence A005849 in OEIS).
The largest known Cullen prime is 6679881•26679881+1 and the largest known generalized Cullen prime is 2525532•732525532+1.
Current status
See also
External links
- Top 20 Cullen Primes
- Top 20 Generalized Cullen Primes
- Web archive of The Chronology of Prime Number Records
- Web archive "prothsearch.net"
- Generalized Cullen Search, Günter Löh (3 ≤ base ≤ 100), dated Sept. 2017
- Web archive "primzahlenarchiv.de", Daniel Hermle (101 ≤ base ≤ 200), dated 2007
- Generalized Cullen, Steven Harvey (101 ≤ base ≤ 10000), dated 2017
- Cullen number
- Mathworld
- The Prime Glossary
