| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Navigation
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Cullen number"
(cat. changed) |
(→Cullen primes: Update largest Gen Cullen prime) |
||
| Line 6: | Line 6: | ||
''C<sub>n</sub>'' is [[prime]] for ''n'' = 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 ''n'' < {{Num|17200000}} ({{OEIS|l|A005849}}). | ''C<sub>n</sub>'' is [[prime]] for ''n'' = 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 ''n'' < {{Num|17200000}} ({{OEIS|l|A005849}}). | ||
| − | The largest known Cullen prime is {{PP|89536|{{Num|6679881}} × 2<sup>{{Num|6679881}}</sup> + 1}} and the largest known generalized Cullen prime is {{PP| | + | The largest known Cullen prime is {{PP|89536|{{Num|6679881}} × 2<sup>{{Num|6679881}}</sup> + 1}} and the largest known generalized Cullen prime is {{PP|129893|{{Num|2805222}} × 25<sup>{{Num|2805222}}</sup> + 1}}. |
==Current status== | ==Current status== | ||
Revision as of 12:54, 2 October 2020
| Last update: 2019-02-27 |
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 < 17,200,000 (sequence A005849 in OEIS).
The largest known Cullen prime is 6,679,881 × 26,679,881 + 1 and the largest known generalized Cullen prime is 2,805,222 × 252,805,222 + 1.
Current status
See also
External links
- Top 20 Cullen Primes
- Top 20 Generalized Cullen Primes
- 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
