For example $8$ is in the middle of the interval between $5$ and $11$, $9$ is at equal distance between $7$ and $11$; $10$ between $7$ and $13$.
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If so, then every even number is a sum of two primes. But this is a notorious open problem, known as the Goldbach conjecture.
1 is a positive nonprime number not between any prime numbers at all. If you consider that cheating (I wouldn't know why), then see Gerry Myerson's anwer.
Check out a related theory: 'Green-Tao Theorem' which is a special case of Erdős conjecture and 'Primes in arithmetic progression' - in short, the primes contain arbitrarily long arithmetic progressions.
protected by t.b. Jul 28 '12 at 13:30
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