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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 OEIS)

Interprimes cannot be prime themselves (otherwise the primes would not have been consecutive). In fact, all interprime are a multiple of 2 or 3.

There are infinitely many primes and therefore also infinitely many interprimes. The largest known interprime as of 2009 may be the 100355-digit n = 65516468355 · 2333333, where n ± 1 is the largest known twin prime.


See also

Prime gap
Twin primes
Cousin prime
Sexy prime

External links

Weisstein, Eric W., "Interprime", MathWorld.

Mathematics Encyclopedia

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