First numbers that belong to both sets:
2,
3,
7,
11,
17,
23,
41,
47,
71,
101,
107,
127,
211,
227,
307,
311,
317,
347,
401,
443,
701,
743,
1117,
1201,
1217,
1277,
1301,
1327,
1427,
1471,
1721,
1777,
2003,
2017,
2027,
2111,
2141,
2207,
2243,
2411,
2417,
2441,
2447,
2477,
2711,
2741,
2777,
3011,
3041,
3203,
3221,
3271,
3307,
3347,
3371,
3407,
4001,
4007,
4127,
4211,
4217,
4241,
4271,
4421,
4441,
4447,
4703,
4721,
7001,
7043,
7121,
7127,
7177,
7211,
7247,
7307,
7321,
7417,
7727,
10007,
10111,
10211,
10247,
10271,
10301,
10343,
10427,
10711,
11027,
11071,
11117,
11171,
11177,
11411,
11447,
11717,
11777,
12007,
12011,
12041,
12071,
12107,
12203,
12227,
12277,
12347,
12377,
12401,
12721,
12743,
14071,
14107,
14177,
14207,
14303,
14321,
14347,
14401,
14447,
14717,
14741,
17021,
17027,
17047,
17077,
17207,
17321,
17401,
17417,
17471,
17707,
17747,
20021,
20071,
20101,
20107,
20147,
20177,
20201,
20327,
20341,
20407,
20411,
20441,
20477,
20717,
20747,
20771,
21001,
21011,
21017,
21101,
21143,
21221,
21317,
21341,
21347,
21377,
21401,
21407,
21701,
21727,
22247,
22271,
22277,
22307,
22441,
22717,
22721,
23017,
23027,
23041,
23071,
23117,
23201,
23321,
23327,
23417,
23447,
23741,
24107,
24317,
24371,
24443,
27017,
27077,
27107,
27127,
27271,
27407,
27701,
40127,
40241,
40277,
40343,
40427,
40771,
41077,
41117,
41141,
41177,
41201,
41341,
41411,
41771,
41777,
42017,
42071,
42101,
42221,
42407,
42701,
42727,
43201,
43271,
43403,
43427,
43721,
43777,
44027,
44111,
44171,
44201,
44207,
44221,
44417,
44711,
44741,
44771,
44777,
47111,
47147,
47207,
47303,
47317,
47407,
47417,
47701,
47711,
47741,
47777,
70001,
70111,
70121,
70241,
70271,
71011,
71171,
71317,
71327,
71411,
71471,
71711,
71777,
72047,
72101,
72211,
72221,
72227,
72271,
72307,
72341,
73121,
73277,
73327,
73417,
73727,
74021,
74027,
74047,
74071,
74177,
74201,
74377,
74411,
74471,
74717,
74747,
74771,
77003.
Some larger examples :
772001,
772127,
772771,
773021,
773027,
773117,
773147,
773207,
773371,
773447,
773777,
774047,
774071,
774107,
774377,
774427,
777001,
777011,
777041,
777317.