A064792 Add more digits to n-th prime (zeros are permitted) until reach another prime.

23, 31, 53, 71, 113, 131, 173, 191, 233, 293, 311, 373, 419, 431, 479, 5303, 593, 613, 673, 719, 733, 797, 839, 8923, 971, 1013, 1031, 10709, 1091, 11311, 1277, 1319, 1373, 1399, 1493, 1511, 1571, 1637, 16703, 1733, 17903, 1811, 1913, 1931, 1973