Interprime
Average of two consecutive odd primes
In mathematics, an interprime is the average of two consecutive odd primes.[1] For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are:
- 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, ... (sequence A024675 in the OEIS)
Interprimes cannot be prime themselves (otherwise the primes would not have been consecutive).[1]
Since there are infinitely many primes, there are also infinitely many interprimes.
See also
- Prime gap
- Twin primes
- Cousin prime
- Sexy prime
- Balanced prime – a prime number with equal-sized prime gaps above and below it
References
- ^ a b Weisstein, Eric W. "Interprime". mathworld.wolfram.com. Retrieved 2020-08-10.
- v
- t
- e
Prime number classes
- Fermat (22n + 1)
- Mersenne (2p − 1)
- Double Mersenne (22p−1 − 1)
- Wagstaff (2p + 1)/3
- Proth (k·2n + 1)
- Factorial (n! ± 1)
- Primorial (pn# ± 1)
- Euclid (pn# + 1)
- Pythagorean (4n + 1)
- Pierpont (2m·3n + 1)
- Quartan (x4 + y4)
- Solinas (2m ± 2n ± 1)
- Cullen (n·2n + 1)
- Woodall (n·2n − 1)
- Cuban (x3 − y3)/(x − y)
- Leyland (xy + yx)
- Thabit (3·2n − 1)
- Williams ((b−1)·bn − 1)
- Mills (⌊A3n⌋)
- Fibonacci
- Lucas
- Pell
- Newman–Shanks–Williams
- Perrin
- Palindromic
- Emirp
- Repunit (10n − 1)/9
- Permutable
- Circular
- Truncatable
- Minimal
- Delicate
- Primeval
- Full reptend
- Unique
- Happy
- Self
- Smarandache–Wellin
- Strobogrammatic
- Dihedral
- Tetradic
- Twin (p, p + 2)
- Bi-twin chain (n ± 1, 2n ± 1, 4n ± 1, …)
- Triplet (p, p + 2 or p + 4, p + 6)
- Quadruplet (p, p + 2, p + 6, p + 8)
- k-tuple
- Cousin (p, p + 4)
- Sexy (p, p + 6)
- Chen
- Sophie Germain/Safe (p, 2p + 1)
- Cunningham (p, 2p ± 1, 4p ± 3, 8p ± 7, ...)
- Arithmetic progression (p + a·n, n = 0, 1, 2, 3, ...)
- Balanced (consecutive p − n, p, p + n)
This number theory-related article is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e