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). In fact, all interprimes are multiples of 2 and/or 3.

There are infinitely many primes and therefore also infinitely many interprimes. The largest known interprime as of 2011 may be the 200700-digit n = 3756801695685 · 2⁶⁶⁶⁶⁶⁹, 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.