A068863 a(1) = 2; a(n+1) is the smallest prime not already in the sequence which differs from a(n) at every digit.

2, 3, 5, 7, 11, 23, 17, 29, 13, 31, 19, 37, 41, 53, 47, 59, 43, 61, 73, 67, 71, 83, 79, 97, 89, 101, 223, 107, 211, 103, 227, 109, 233, 127, 239, 113, 229, 131, 257, 139, 241, 137, 251, 149, 263, 151, 269, 157, 271, 163, 277, 181, 293, 167, 281, 173, 307, 179