A number n is called lonely if it sets a new record for the distance to the nearest prime number.
For example, 1E is a lonely number, since it is 4 away from a prime, namely 17, and no number less than 1E is 4 or more away from a prime. (The prime 1E itself is ignored.)
The sequence of lonely numbers begins: 0, 1E, 45, X0, 157, 938, 939, 93X, 93E, 940, 1317, 2367, 9108, 9109, 9341, E442, E443, 12075, 16230, 16231, 16232.
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Numbers aplenty, Lonely numbers