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I know, I know, yet another primes challenge...
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A lonely (or isolated) prime is a prime number p such that p-2, p+2, p-4, p+4 ... p-2k, p+2k for some k are all composite. We call such a prime a kth-times-isolated prime.
For example, a 5th-times-isolated prime is 211, since all of 201, ...