A clock prime is a prime number obtained by the concatenation of one or more consecutive hour labels of a 12-hour analog clock, keeping 10, 11, and 12 complete and unreversed. The reading starts at any hour, proceeds in one direction, and may continue for more than one revolution. In a clockwise direction, the primes are 2, 3, 5, 7, 11, 23, 67, 89, 4567, 23456789, 23456789101112123, ... (OEIS A036342). In a counterclockwise direction, the primes are 2, 3, 5, 7, 11, 43, 109, 10987, 76543, 6543211211, 4321121110987, ... (OEIS A036343). In either direction, the primes are 2, 3, 5, 7, 11, 23, 43, 67, 89, 109, 4567, 10987, 76543, 23456789, 6543211211, ... (OEIS A036344).
Reading a valid 24-hour digital clock display from 00:00 through 23:59 as an integer, with the colon omitted and leading zeros ignored, gives 211 possible prime values: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 101, ... (OEIS A050246).
