First numbers that belong to both sets:
11,
29,
41,
43,
61,
101,
227,
229,
281,
601,
661,
809,
821,
881,
2267,
4001,
4229,
8009,
8221,
8821,
26881,
40427,
220021,
404249,
600881,
602081,
6600227,
6866683,
8608081,
228440489.