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Interprime

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]

There are infinitely many primes and therefore also infinitely many interprimes. The largest known interprime as of 2018 may be the 388342-digit n = 2996863034895 · 21290000, where n + 1 is the largest known twin prime.[2]

See also

References

  1. ^ a b Weisstein, Eric W. "Interprime". mathworld.wolfram.com. Retrieved 2020-08-10.
  2. ^ Caldwell, Chris K. "The Top Twenty: Twin Primes". The Prime Pages. Retrieved 27 February 2017.


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