Cullen number
Last update: 2019-02-27 |
A Cullen number C_{n} is a number of the form n × 2^{n} + 1,
a generalized Cullen number base b is a number of the form n × b^{n} + 1. (perhaps own page?)
Cullen primes
C_{n} 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 × 2^{6,679,881} + 1 and the largest known generalized Cullen prime is 1,806,676 × 41^{1,806,676} + 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