In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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, ...
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 may be the 388342-digit ''n'' = 2996863034895 · 2
1290000, where ''n'' + 1 is the largest known
twin prime.
See also
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Prime gap
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Twin primes
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...
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Cousin prime
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Sexy prime
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Balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p_n, where is it ...
– a prime number with equal-sized prime gaps above and below it
References
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Integer sequences
Prime numbers
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