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I'm not sure what you're asking. The smallest number that can't be between two primes is obviously 1. Once you start running into primes, every composite number is between at least two primes.

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Q: What is the smallest integer that cannot occur between two primes?
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What is the least positive number that is divisible by three different primes?

30, which is the smallest positive integer divisible by the first three primes: 2, 3 and 5.


What is the least number that has three different prime factors?

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