Interprime

In mathematics, an interprime is the average of two consecutive odd primes. 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).
There are infinitely many primes and therefore also infinitely many interprimes. The largest known interprime as of 2011[update] may be the 200700-digit n = 3756801695685 · 2666669, where n ± 1 is the largest known twin prime.
See also[edit]

Prime gap
Twin primes
Cousin prime
Sexy prime

External links[edit]

Weisstein, Eric W. “Interprime”. MathWorld. 

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Prime number classes

By formula

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 (2u·3v + 1)
Quartan (x4 + y4)
Solinas (2a ± 2b ± 1)
Cullen (n·2n + 1)
Woodall (n·2n − 1)
Cuban (x3 − y3)/(x − y)
Carol (2n − 1)2 − 2
Kynea (2n + 1)2 − 2
Leyland (xy + yx)
Thabit (3·2n − 1)
Mills (floor(A3n))

By integer sequence

Fibonacci
Lucas
Pell
Newman–Shanks–Williams
Perrin
Partitions
Bell
Motzkin

By property

Wieferich (pair)
Wall–Sun–Sun
Wolstenholme
Wilson
Lucky
Fortunate
Ramanujan
Pillai
Regular
Strong
Stern
Supersingular (elliptic curve)
Supersingular (moonshine theory)
Good
Super
Higgs
Highly cototient

Base-dependent

Happy
Dihedral
Palindromic
Emirp
Repunit (10n − 1)/9
Permutable
Circular
Truncatable
Strobogrammatic
Minimal
Weakly
Full reptend
Unique
Primeval
Self
Smarandache–Wellin

Patterns

Twin (p, p + 2)
Bi-twin chain (n − 1, n + 1, 2n − 1, 2n + 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 (p, 2p + 1)
Cunningham chain (p, 2p ± 1, …)
Safe (p, (p − 1)/2)
Arithmetic progression (p&

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