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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).

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.

Prime gap
Twin primes
Cousin prime
Sexy prime