Nexus prime (number)
In number theory, a nexus prime is a prime of the form bp − (b−1)p with odd prime p. Cases with p = 3 are cuban primes. Cases with b = 2 are Mersenne primes. A nexus number is a number of form bn − (b−1)n.[1]
Smallest nexus prime[edit]
The first odd prime p such that bp − (b−1)p is (probable) prime for b = 2, 3, 4, 5, ... are
- 3, 3, 3, 3, 5, 3, 7, 7, 3, 3, 3, 17, 3, 3, 43, 5, 3, 1607, 5, 19, 127, 229, 3, 3, 3, 13, 3, 3, 149, 3, 5, 3, 23, 3, 5, 83, 3, 3, 37, 7, 3, 3, 37, 5, 3, 5, 58543, 3, 3, 7, 29, 3, 479, 5, 3, 19, 5, 3, 4663, 54517, 17, 3, 3, 5, 7, 3, 3, 17, 11, 47, 61, 19, ... (sequence A125713 in the OEIS)
The first b such that bp − (b−1)p is (probable) prime for odd prime p = 3, 5, 7, 11, ... are
- 2, 2, 2, 6, 2, 2, 2, 6, 3, 2, 40, 7, 5, 13, 3, 3, 2, 7, 18, 47, 8, 6, 2, 26, 3, 42, 2, 13, 8, 2, 8, 328, 8, 9, 45, 27, 13, 76, 15, 52, 111, 5, 15, 50, 287, 16, 5, 40, 23, 110, 368, 23, 68, 28, 96, 81, 150, 3, 143, 4, 12, 403, 4, 45, 11, 83, 21, 96, 5, 109, 350, ... (sequence A103794 in the OEIS)
Largest known[edit]
The largest known nexus primes are Mersenne primes. As of September 2018[update], the largest known other nexus (probable) prime is 8615997 − 7615997.[2]
References[edit]
- ↑ Weisstein, Eric W. "Nexus Number". MathWorld. Retrieved 30 September 2018.
- ↑ PRP Top
External links[edit]
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