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Difference between revisions of "Cullen number"
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| − | + | A '''Cullen number''' {{V|C<sub>n</sub>}} is a number of the form {{Kbn|+|n|2|n}}, | |
| − | A '''Cullen number ''C<sub>n</sub> | + | |
| − | a '''generalized Cullen number''' base | + | a '''generalized Cullen number''' base {{Vb}} is a number of the form {{Kbn|+|n|b|n}}. '''(perhaps own page?)''' |
==Cullen primes== | ==Cullen primes== | ||
| − | + | {{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|{{ | + | The largest known Cullen prime is {{PP|89536|{{Kbn|+|6679881|6679881}}}} and the largest known generalized Cullen prime is {{PP|129893|{{Kbn|+|2805222|25|2805222}}}}. |
==Current status== | ==Current status== | ||
| − | *[ | + | *see [[Cullen prime 2|Cullen primes]] |
| + | *see [[PrimeGrid Cullen Prime Search#Status|PrimeGrid Cullen Prime Search]] | ||
==See also== | ==See also== | ||
Latest revision as of 17:39, 31 August 2021
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 < 21,000,000 (sequence A005849 in OEIS).
The largest known Cullen prime is 6679881•26679881+1 and the largest known generalized Cullen prime is 2805222•252805222+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
