A prime is said to be balanced if it is the average of the two surrounding primes, i.e., it is at equal distance from previous prime and next prime.

For example, 53 is a balanced prime since it is the average of the two primes 47 and 59.

The smallest 3 × 3 magic square made of balanced primes is

The first balanced primes are 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511 more terms